III SEMESTER CORE COURSE

Transcription

1 BA PHILOSOPHY PROGRAMME III SEMESTER CORE COURSE SYMBOLIC LOGIC AND INFORMATICS ( 2014 Admission onwards) (CU-CBCSS) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Calicut university P.O, Malappuram Kerala, India

2 CONTENTS 1. Preface 2. Objectives, Highlights and References 3. Pattern of Question Paper 4. Module I - Introduction 5. Module II - Truth functional Connectives 6. Module III - Statement Forms and Argument Forms 7. Module IV - Formal Proof of Validity 8. Module V - Informatics 9. Model Question Paper 10. Question Bank for Internal Assessment 11. Team of Teachers SYMBOLIC LOGIC AND INFORMATICS Page 2

3 PREFACE You are already familiar with the study materials for the Core Course PHL2B02 - Logic and Scientific Method of the II Semester B. A. Philosophy Programme. The study materials in this section are for the Core Course IV - PHL3B04 Symbolic Logic and Informatics of the III Semester B. A. Philosophy Programme in the SDE stream. This course is designed to make the learners familiar with the more advanced level of logic in which we use symbolic language and signs for making logical operations more precise and clear. Hence, it is necessary to keep in mind the points of continuity between the two courses on logic - PHL2B02 and PHL3B04. Informatics is another key component of this course, and this will enable you to grasp the correlation between logic and computer language or the binary logic of computer language. A keen study of these courses on Logic will definitely guide you to detect the common ambiguities and fallacies in reasoning so that one can express and analyze thoughts and arguments in their most legible and precise form. The modules in the syllabus of this course contain problem-solving exercises in addition to the descriptive topics. Hence, the learner is required to do much deskwork on the basis of the theoretical lessons in the modules. The content of each module is prepared according to the approved model question paper. The Question Bank for conducting the Internal Evaluation also forms a part of the course materials. The Part A of the question paper for examination contains MCQs in the model of those given in the Question Bank. With all the best wishes for your careful and confident performance in the examinations, Dr. M. Ramakrishnan Coordinator (Chairperson, Board of Studies in Philosophy) SYMBOLIC LOGIC AND INFORMATICS Page 3

4 OBJECTIVES Module I To introduce the main differences between traditional and symbolic logic. To grasp and experience the advantages of symbolization. To learn the different symbols for various logical functions. Module II To delineate the distinction between simple and compound statements. To learn how to construct the truth tables for different types of compound statements. To practise problem solving exercises involving truth tables. To get an overview of De-Morgan s theorem. Module III To familiarize with the distinction between argument and argument form and between statement and statement form. To introduce the distinction between validity and invalidity. To familiarize with the logical classification of statements. Module IV To grasp and analyze the characteristics of formal proof of validity. To familiarize with the nine rules of inference. To practise the technique of proving the validity of deductive arguments by applying the nine rules. Module V To introduce the definition and scope of informatics. To define the terms like data, information and knowledge in the domain of informatics. To make an analytic study of the emerging ethical issues in the cyber world. To introduce logic gates as the meeting point between symbolic logic and computer language. SYMBOLIC LOGIC AND INFORMATICS Page 4

5 HIGHLIGHTS MODULE 1 - Introduction 1.1 Traditional logic and symbolic logic- Differences 1.2 Advantages of symbolization. 1.3 The symbols for Conjunction, Negation and Disjunction. MODULE 2 - Truth functional connectives 2.1. Compound statements a) Difference between simple and compound statements b) Truth functional compound statement 2.2. Truth tables for conjunction and negation a) Finding truth values of statements containing conjunction and negation 2.3. Disjunction a) Truth table for disjunction b) Finding truth values of statements containing disjunction, conjunction and negation 2.4. Implication a) Truth table for implication b) Finding truth values of statements containing implication, disjunction, conjunction and negation 2.5. Equivalence a) Material equivalence b) Biconditional c) Logical equivalence- truth table for De-Morgan s theorem MODULE 3 - Statement Forms and argument forms 3.1. Argument form- Definition, validity and invalidity 3.2. Substitution instance and specific form- Definitions 3.3. Statement forms and statements a) Definitions b) Classification of statements into tautology, contradictory and contingent MODULE 4 - Formal proof of validity 4.1. Definition 4.2. Nine rules of inference MODULE 5 - Informatics 5.1. Etymology and definition 5.2. Data, information and knowledge 5.3. Issues in cyber ethics - reduced privacy, cyber addiction and information overload 5.4. Logic Gates SYMBOLIC LOGIC AND INFORMATICS Page 5

6 References: Websites: 1. Symbolic Logic, IM Copi (Module 1-4) 2. Wikipedia Online Encyclopaedia (Section 5.1) 3. Informatics, Siny G Benjamin (Section 5.2 and 5.3) 4. Philosophy and Computing: An Introduction, Luciano Floridi (Section 5.4) 5. Alan Evans et.al. Informatics:Technology in Action. Delhi: Pearson, Digital Logic design by: Dr. Wa el Al Qassas, Al Albayt University _lectures.pdf SYMBOLIC LOGIC AND INFORMATICS Page 6

7 Pattern of Question Paper Duration Section Pattern Total number of questions 3Hrs A Objective Type B C D Multiple choice questions Short Answer questions Paragraph Answer questions Essay questions Questions to be answered Marks for each question Total marks for each section ½ 10 x ½ = x 3 = x 5 = x 15 = 30 TOTAL = 80 Time: Three Hours Maximum: 80 marks PART - A - Multiple-choice questions Answer all questions. Each question carries ½ marks. (10 x ½ = 5marks) PART - B - Short answer questions Answer any five out of the eight questions. Each question carries 3 marks. (5 x 3 = 15 marks) PART - C - Paragraph answer questions Answer any six out of the nine questions. Answer should not exceed 100 words. Each question carries 5 marks. (6x5 =30marks) PART - D - Essay questions Answer any two out of the four questions. Answer should not exceed 1000 words. Each question carries 15 marks. (2 x 15 = 30marks) SYMBOLIC LOGIC AND INFORMATICS Page 7

8 Scrutinized by: Dr. M. Ramakrishnan Former Head of the Dept. of Philosophy Govt. Brennen College, Thalassery (Chairperson, Board of Studies in Philosophy, University of Calicut) Prepared by: Module 1 Module II Module III Dr. K. Syamala Head of the Dept. of Philosophy Sree Sankaracharya University of Sanskrit, Regional Center Edat, Payyannur, Kannur (Dt.) Dr. Sirajul Muneer. C Assistant Professor of Philosophy Sree Sankaracharya University of Sanskrit, Regional Center Edat, Payyannur, Kannur (Dt.) Ms. Priya Assistant Professor of Philosophy Govt. Brennen College Thalassery Module IV Dr. Smitha T. M. Assistant Professor of Philosophy Maharaja s College, Ernakulum Cochin smithanil2010@gmail.com Layout: Computer Section, SDE Reserved SYMBOLIC LOGIC AND INFORMATICS Page 8

9 CONTENTS PAGES MODULE 1 10 MODULE 1I 17 MODULE III 25 MODULE 1V 33 MODULE V 43 SYMBOLIC LOGIC AND INFORMATICS Page 9

10 MODULE 1 INTRODUCTION For model questions, see the Question Bank. PART - A - Multiple-choice questions PART - B - Short answer questions 1. Summarize the main benefits of using symbolic language in logic. Logicians make use of constant and variable symbols mainly to avoid the linguistic defects in making and examining arguments. By replacing linguistic expressions with symbols, an argument becomes more explicit without ambiguity. Symbolic language helps logicians to determine the validity of an argument more easily and accurately. With symbolic language, we can also maintain economy and precision of arguments. 2. What are the difficulties faced by logicians while presenting an argument in ordinary language? While presenting an argument in natural languages, the words used may be vague or equivocal. In ordinary language expressions, metaphors and idioms may often create confusion. Ordinary language expressions are not always free from emotional appeal, but logicians are not concerned with such expressions. These difficulties can be avoided by using symbolic language in logic. 3. Define conjunction. A compound statement formed by inserting the word and between the two component statements is called a conjunction. The two statements so combined are called conjuncts. In symbolic logic, the dot is the special symbol for conjunction. E.g. p. q. 4. What do you mean by a disjunctive proposition? Two simple propositions when combined by either -- or forms a disjunctive proposition. The two component propositions so combined are called disjuncts. The symbol for disjunction is. For example, Either you can go to the park or you can watch the TV. Its symbolic representation is P v T. 5. Define negation. Negation is the logical function of denying a fact. A negative proposition shows that It is not the case that p and the symbolic form is ~p. 6. Distinguish between simple proposition and compound proposition. A simple proposition is the one which does not contain any other statement as a component. For example, Roses are red symbolized by R. A compound proposition is the SYMBOLIC LOGIC AND INFORMATICS Page 10

11 one that contains another statement as a component. Compound propositions are mainly conjunctive, disjunctive, implicative and biconditional. Their symbolic forms are the following: Conjunction p. q Disjunction Implication Biconditional p v q p כ q p q 7. Name the different types of compound propositions. Or Present the symbolic forms of compound propositions. The main types of compound statements are Conjunction, disjunction, implication and biconditional. Their symbolic forms are the following: Conjunction p.q Disjunction Implication Biconditional p v q p כ q p q 8. Write a short note on constant symbols. In symbolic logic, we use definite signs to represent logical relations. Constant symbols do not change their value throughout the domain of logic. Common constant symbols used in logic are the following: Negation ~ Conjunction. Disjunction Implication Biconditional v 9. What is the main difference between variable symbols and constant symbols? In symbolic logic, variable symbols keep on changing their value from argument to argument. They do not have fixed values. Constant symbols do not change their value throughout the domain of logic. SYMBOLIC LOGIC AND INFORMATICS Page 11

12 Variables are represented by letters like p, q etc. Constant symbols are the following: Conjunction Disjunction Implication v Biconditional Negation ~ 10. Match the following: a) If -- then - Equivalence b) ~ M - Weak c) Biconditional - Implication d) Inclusive disjunction - Negation Answers: a) Implication b) Negation c) Equivalence d) Weak PART - C - Paragraph answer questions 1. What are the advantages of using symbols in logic? Symbols are useful to logicians in many ways. Firstly, the logical form of an argument becomes explicit by using symbols. By using symbols to represent ordinary language expressions, the logical form of an argument becomes explicit. It helps us to avoid ambiguous and confusing use of words. By using symbols, we can determine the validity of an argument quickly and accurately. The use of symbols in logic is an economical device. Lengthy and complicated arguments become small and precise by symbolization. Symbolization offers specific methods of testing the validity of arguments like truth table method and formal proof of validity. Thus, symbolic logic has the advantages of clarity, brevity and accuracy over traditional logic. It drastically reduces the space, time and energy needed for logical operations. 2. Distinguish between variable symbols and constant symbols. In the traditional logic, only three variable symbols are used, that is S, P and M for the subject, predicate and middle term in a categorical syllogism. A, E, I, O are symbols for the four types of categorical propositions. In modern logic, the use of symbols is more extensive to make it symbolic logic. In symbolic logic, we use two types of symbols - variables and constants. A variable symbol keeps on changing its value from argument to argument. These symbols are dummies that stand for terms and concepts. They do not SYMBOLIC LOGIC AND INFORMATICS Page 12

13 have fixed values. For example, the symbol P in one argument may stand for You will pass, in another argument for It is a pleasant day, and yet in a third argument for We will go for picnic today. Hence, the symbol P may have different meanings in different contexts. Many types of variables are used in modern logic such as propositional variables, predicates variables, class variables etc. Modern logicians began to use constant symbols that gave them the advantage of clarity, brevity and accuracy over traditional logic. Constant symbols do not change their value throughout the domain of logic. Common constant symbols used in logic are the following: Negation ~ Conjunction Disjunction N Implication Biconditional v 3. What do you mean by truth functional connectives? The truth-value of a truth functional compound statement is determined by the truth-value of its components. Logical constants are the connecting symbols between the component statements. They show how the component statements are related. The truth-values of the component statements along with the nature of truth functional connective determine the truth-value of the compound statement. There are four types of truth functional connectives. They are conjunction, disjunction, implication and biconditional or equivalence. Their symbolic forms are given below: Conjunction Disjunction Implication Biconditional v 4. Symbolize the following using the letters given in brackets. a) Beethoven and Mozart were great composers (B, M) SYMBOLIC LOGIC AND INFORMATICS Page 13

14 b) Either we will reduce poverty, or we will provide subsidies. (R, P) c) If hydrogen is combined with oxygen in a specific ratio, water is produced. (H, W) d) Salim will not attend the function. (S) Answers: a) B M b) R v P c) H W d) ~S 5. Symbolize the following. a) If p then q and r. b) Neither a nor b. c) It is not the case that either k or t. d) If both a and b then both c and d. Answers: a) p (q r), b) ~a v ~b, c) ~ (k v t), d) (a b) (c d) 6. Write a note on the symbolization and truth function of conjunction. When two statements are joined by placing and between them, the resulting statement is a conjunction. The component statements are called the conjuncts. The (dot) symbol represents conjunction. Where p and q are statement variables representing any two statements, their conjunction is represented as p q. If p represents The city is heavily populated and q represents There is an outbreak of fever, then p q represents their conjunction The city is heavily populated and there is an outbreak of fever. A conjunctive statement is true only if both of its conjuncts are true. p q is true only if both p is true and q is true. Hence, the truth-value of p q is determined by the truthvalues of both p and q. 7. Write a note on disjunction and distinguish between inclusive and exclusive disjunction. When two statements are combined by inserting or between them, the resulting compound statement is a disjunction or alternation. The two statements thus combined are called disjuncts or alternatives. The symbol v called a wedge or a vee is used for indicating disjunction. The disjunctive proposition Either a disease is hereditary or it is due to infection is symbolized as - H v I The word or may be used in the weak or strong sense. Weak disjunction is called inclusive because if both or at least one of the disjuncts is true the disjunction is true and it is false only if both the disjuncts are false. E.g., Leave will be granted either in the case of sickness or bus strike. Here, leave is granted on either one of the conditions or both the conditions. Hence, the disjunction is weak. In strong disjunction, or is used in the exclusive sense. It means at least one and at most one. That is only one of the disjuncts but not both will be true at a time. E.g., I shall take either coffee or tea. Here, it is clear that I want to take only one of the two options but not both. Hence, the disjunction is strong. SYMBOLIC LOGIC AND INFORMATICS Page 14

15 Part - D - Essay questions 1. Explain the salient features of symbolic logic and bring out its differences from traditional logic. Or Bring out the main advantages of using symbols in logic. Add a note on the different types of symbols used by modern logicians. Logic is defined as the science of valid reasoning. An argument or a piece of reasoning is a relational arrangement of premises and conclusion. Hence, the validity and correctness of an argument is ensured when the premises are strong enough to support the conclusion. Arguments formulated in English or any other natural language are often confusing because of the vague and equivocal nature of the words in which they are expressed. Misleading idioms and emotional expressions make them vague. To avoid such difficulties connected with ordinary language, logicians have developed specialized technical symbols to represent logical sentences and arguments. The works of philosophers like Russell have introduced symbolic logic that enables us to overcome the limitations of traditional logic. Aristotle made use of certain symbols that had been used in traditional logic. Modern logicians have introduced more specialized symbols that make logical analysis more easy and accurate. The differences between old and new logic is one of degree rather than kind. The special symbols in modern logic enable us to attain more clarity and precision in presenting arguments. Symbolic expressions help us to avoid the problems of vagueness and confusion of meaning. According to A. N. Whitehead, By the aid of symbolism, we can make transitions in reasoning almost mechanically by eye. The use of symbols in logic gives us many advantages: Firstly, the logical form of an argument becomes explicit by using symbols. By replacing language by symbols, the logical form of an argument becomes clear. When the logical form of an argument is clear, it is easy to determine its validity. The symbolic form of an argument makes logical analysis more quick and accurate. Symbolization offers specific methods of testing the validity of arguments like truth table method and formal proof of validity. Thus, symbolic logic has the advantages of clarity, brevity and accuracy over traditional logic. It drastically reduces the space, time and energy needed for logical operations. The use of symbols in logic is also an economy device. The long and big arguments become precise and clear through symbolization. This will help us to reduce the chances of committing error in deciding their validity. In the traditional logic, only three variable symbols are used, that is S, P and M for the subject, predicate and middle term in a categorical syllogism. A, E, I, O are symbols for the four types of categorical propositions. In modern logic, the use of symbols is more extensive to make it symbolic logic. In symbolic logic, we use two types of symbols - variables and constants. A variable symbol keeps on changing its value from argument to argument. These symbols are dummies that stand for terms and concepts. They do not have fixed values. For example, the symbol P in one argument may stand for You will SYMBOLIC LOGIC AND INFORMATICS Page 15

16 pass, in another argument for It is a pleasant day, and yet in a third argument for We will go for picnic today. Hence, the symbol P may have different meanings in different contexts. Many types of variables are used in modern logic such as propositional variables, predicates variables, class variables etc. Modern logicians began to use constant symbols that gave them the advantage of clarity, brevity and accuracy over traditional logic. Constant symbols do not change their value throughout the domain of logic. Common constant symbols used in logic are the following: Negation ~ Conjunction Disjunction Implication Biconditional v The main differences between traditional and symbolic logic are summarized below: i) Traditional logic is concerned more with the relation of the subject and predicate terms of propositions. Symbolic logic is more concerned with propositions as a unit and propositional relations. ii) Traditional logic is concerned with both form and matter of thought whereas symbolic logic is purely formal in nature. iii) Traditional logic has only a limited use of symbols, whereas there is an extensive use of special symbols in symbolic logic. iv) Syllogisms are central in Aristotelian logic. Instead, the internal structure of propositions and arguments is the focus of modern logic. Hence, the set of symbols include not only variable symbols but also the constants that represent logical connections. v) Traditional logicians use non-mathematical methods to determine the validity of arguments. Modern logicians adopt decision procedures that ensure mathematical precision in analyzing arguments. In spite of all the above differences, modern logic is not opposed to traditional logic. It is a much improved form of traditional logic. We can say that what was implicit in Aristotelian logic has become explicit in modern logic. The aim of all logicians, traditional as well as modern, is to provide methods or devices to differentiate between correct and incorrect reasoning. The difference between classical logic and symbolic logic is only of degree rather than of kind. SYMBOLIC LOGIC AND INFORMATICS Page 16

17 MODULE 2 TRUTH FUNCTIONAL CONNECTIVES PART - A - Multiple-choice questions For model questions, see the Question Bank. PART - B - Short answer questions 1. What is an atomic/simple proposition? All propositions are either atomic or molecular. An atomic proposition is one which does not contain any other proposition as its component. An atomic proposition cannot be divided into further component propositions. For example, Ramesh is honest which is symbolized as H. Atomic proposition is also known as simple proposition because it does not contain any other statement as its component. 2. Define compound proposition. A compound proposition is that which contains two or more propositions as its components. Compound proposition is also known as molecular proposition. Ramesh is honest and Dinesh is intelligent is a compound proposition. It contains two simple propositions as its components. Compound propositions may be conjunctive, disjunctive, or implicative. 3. Define compound statement and present the symbolic form of its different types. A compound proposition is that which contains two or more propositions as its components. Compound proposition is also known as molecular proposition. The main types of compound statements are Conjunction, disjunction, implication and biconditional. Their symbolic forms are the following: Conjunction Disjunction Implication Biconditional p q p v q p כ q p q 4. Define Implication. Implication is the truth-functional relation between two simple propositions connected by the phrase if -- then. For example, If it rains, then the road will be wet. The part of proposition that lies in between if and then is called the antecedent. That which follows SYMBOLIC LOGIC AND INFORMATICS Page 17

18 the word then is called the consequent. The symbol called horseshoe is used to form an implicative statement. The symbolic form of an implicative proposition is as follows: P Q 5. Define conjunction. Conjunction is a compound proposition in which the word and connects simple statements. To connect statements conjunctively, the dot symbol is used. E.g. John is intelligent and John is attentive is symbolized as I A In conjunction, if both its conjuncts are true, the conjunction is true, otherwise, it is false. 6. Define negation. Negation is the denial of a statement formed by inserting not to show the denied part. A negative statement means it is not the case that. The negation of P is it is not the case that P. The symbol ~ called curl or tilde is used to indicate negation. E.g. ~ P Logicians treat negation as a truth functional operator rather than a connective because negation applies directly to a single proposition. 7. Define disjunction. Disjunction is a truth-functional connective that indicates an or relationship between two propositions. The component statements are called disjuncts. The symbol for disjunction is a wedge. E.g. Either John is careless or John is ignorant is symbolized as C v I. Present the truth table for material equivalence. Two sentences are said to be materially equivalent when they have the same truth-value. The symbol called the tribar stands for material equivalence. The truth table for biconditional or material equivalence is as follows: P Q P Q T T T T F F F T F F F T 8. Match the following: a) Conjunction - Wedge b) Disjunction - Tribar c) Negation - Horseshoe d) Implication - Tilde e) Bi-conditional - Dot SYMBOLIC LOGIC AND INFORMATICS Page 18

19 Ans: a) Dot, b) Wedge, c) Tilde, d) Horseshoe, e) Tribar 9. Explain logical equivalence. When two statements are logically equivalent, each has the same truth-value under the same truth conditions. For example, consider any statement p and its double negation ~ ~ p. The principle of double negation, p ~ ~ p is proved tautologous by the following truth table: P ~ p ~ ~ p p ~ ~ p T F T T F T F F The table proves that the logical equivalence of p is ~ ~ p PART - C - Paragraph answer questions 1. Distinguish between simple and compound proposition. All propositions are either simple or compound or general. A simple proposition is the one which does not contain any other proposition as its component. A simple proposition cannot be split into further component propositions. For example, Ramesh is honest symbolized as H. It does not contain any other statement as a component. Simple proposition is also known as atomic proposition. A compound proposition is that which contains two or more propositions as its components. Ramesh is honest and Dinesh is intelligent is a compound proposition symbolized as H I. It contains two simple propositions as its components. Compound proposition is also known as molecular proposition. The main types of compound statements are Conjunction, disjunction, implication and biconditional. Their symbolic forms are the following: Conjunction p q Disjunction Implication Biconditional p v q p כ q p q 2. Draw the Truth Table for conjunction and negation. Conjunction: Conjunction is a compound proposition in which the word and is used to connect simple statements. To connect statements conjunctively, the dot symbol is used. In SYMBOLIC LOGIC AND INFORMATICS Page 19

20 conjunction, if both its conjuncts are true, the conjunction is true, otherwise, it is false. The truth table for conjunction is as follows: Negation: P Q P Q T T T T F F F T F F F F Negation is a compound proposition in which the word not or the phrase it is not the case that is used. The symbol ~ called curl or tilde is used to form the negation of a statement. The truth table for negation is as follows: P ~p T F F T 3. Describe the distinction between inclusive disjunction and exclusive disjunction. Logicians recognize two kinds of disjunctions, inclusive disjunction and exclusive disjunction. A disjunction containing non-exclusive alternatives is called inclusive disjunction. Example, Ramesh is either intelligent or hard working. The sense of or in inclusive disjunction is at least one, both may be. A disjunction containing exclusive alternatives is called exclusive disjunction. For example, Today is either Wednesday or Thursday. The sense of or in exclusive disjunction is at least one, but not both. The truth table for inclusive disjunction is as follows: P Q P v Q T T T T F T F T T F F F The truth table for exclusive disjunction is as follows: SYMBOLIC LOGIC AND INFORMATICS Page 20

21 P Q P ^ Q T T F T F T F T T F F F 4. State and explain De Morgan s Theorems. There are two logical equivalences that express important interrelations among conjunction, disjunction and negation. Since a conjunction of p and q assert that both its conjuncts are true, to contradict p q is to assert that at least one is false. Thus asserting the negation of the conjunction p q is logically equivalent to asserting the disjunction of the negations of p and of q. This is expressed by the bi-conditional ~ ( p q ) (~ p v ~ q ) which is proved to be a tautology. Similarly, the disjunction p v q asserts that at least one of its two disjuncts is true, it is contradicted only by asserting that both are false. Thus asserting the negation of the disjunction p v q is logically equivalent to asserting the conjunction of the negations of p and of q. This is expressed by the bi-conditional ~ (p v q) (~ p ~ q). These two equivalences are known as De Morgan s theorems. De Morgan s theorem is formulated as: a. The negation of the conjunction of two statements is logically equivalent to the disjunction of their negations. ~ ( p. q ) (~ p v ~ q ) b. The negation of the disjunction of two statements is logically equivalent to the conjunction of their negations. ~ ( p v q) (~ p. ~ q ). For example, It will not both rain and snow tomorrow can be translated as ~ (R S), or it can be translated as ~R ~S. Likewise, It will neither rain nor snow tomorrow can be translated as ~ (R V S) or ~R ~S. 5. Distinguish between material implication and material equivalence. Implication is a compound proposition in which the simple statements are connected by the phrase if -- then. For example, If it rains, then the road will be wet. The part of proposition which lies in between if and then is called the antecedent. The part of proposition which follows the word then is called the consequent. The general form of an implicative proposition is as follows: If antecedent, then consequent. The symbol called horseshoe is used to form an implicative statement. The truth table for logical equivalence is as follows: P Q P Q T T T T F F SYMBOLIC LOGIC AND INFORMATICS Page 21

22 F T T F F T Two sentences are said to be materially equivalent when they have the same truth-value. It is a compound proposition in which the simple statements are connected by the phrase if and only if. The symbol called the tribar stands for material equivalence. Material equivalence is also called Bi-conditional proposition. The truth table for material equivalence is as follows: P Q P Q T T T T F F F T F F F T 6. Distinguish between logical equivalence and material equivalence. In logic, there are important equivalences between statements that are a necessary result of how the logical operators function. When two statements are logically equivalent, each has the same truth-value under the same truth conditions. For example, consider any statement p and its double negation ~ ~ p. The principle of double negation p ~ ~ p is proved to be tautology by the following truth-table: P ~ p ~ ~ p p ~ ~ p T F T T F T F T This proves that the logical equivalence of p is ~ ~ p There is difference between logical equivalence and material equivalence. Two statements are logically equivalent only when it is impossible for the two statements to have different truth-values. Therefore, logically equivalent statements have the same meaning and may be substituted for one another. However, two statements are materially equivalent if they merely happen to have the same truth-value. Statements that are merely materially equivalent certainly cannot be substituted for one another. PART - D - Essay questions 1. Explain the truth functional compound statements using truth tables. All propositions are either simple or compound or general. A simple proposition is that which does not contain any other proposition as its component. A simple proposition cannot be split into further component propositions. For example, the proposition Ramesh SYMBOLIC LOGIC AND INFORMATICS Page 22

23 is honest does not contain any other statement as a component. Simple proposition is also known as atomic proposition. A compound proposition is that which contains two or more propositions as its components. Ramesh is honest and Dinesh is intelligent is a compound proposition. It contains two simple propositions as its components. Compound proposition is also known as molecular proposition. Compound propositions are of different types such as Negative, Conjunctive, Disjunctive, Implicative, and Material Equivalent. Negation: Negation is a compound proposition in which the word not or the phrase it is not the case that is used. Example, Ramesh is not honest or It is not the case that Ramesh is honest. It contains Ramesh is honest as component part.. The symbol ~ called curl or tilde is used to form the negation of a statement. The truth table for negation is as follows: P ~p T F F T Conjunction: Conjunction is a compound proposition in which the word and is used to connect simple statements. To connect statements conjunctively, the dot symbol is used for conjunction. In conjunction, if both its conjuncts are true, the conjunction is true, otherwise, it is false. The truth table for conjunction is as follows: Disjunction: P Q P Q T T T T F F F T F F F F Disjunction is a compound proposition in which the simple propositions are connected by the word or or the phrase either.or. Example, Ramesh is either intelligent or hard working. Today is either Wednesday or Thursday. The components of a disjunction are called disjuncts. Logicians recognize two kinds of disjunction - inclusive disjunction and exclusive disjunction. A disjunction containing non-exclusive alternatives is called inclusive disjunction. Example, Ramesh is either intelligent or hard working. The sense of or in inclusive disjunction is at least one, both may be. A disjunction containing exclusive SYMBOLIC LOGIC AND INFORMATICS Page 23

24 alternatives is called exclusive disjunction. Example, Today is either Wednesday or Thursday. The sense of or in exclusive disjunction is at least one, but not both. The truth table for inclusive disjunction is as follows: P Q P v Q T T T T F T F T T F F F Implication: Implication is a compound proposition in which the simple statements are connected by the phrase if -- then. For example, If it rains, then the road will be wet. The part of proposition which lies in between if and then is called antecedent. The part of proposition which follows the word then is called consequent. The general form of an implicative proposition is as follows: If antecedent, then consequent. The symbol called horseshoe is used to form a implicative statement. The truth table for logical equivalence is as follows: P Q P Q T T T T F F F T T F F T Bi-conditional: Bi-conditional proposition is a compound proposition in which the simple statements are connected by the phrase if and only if. For example, I will go to the cinema if and only if my friend comes with me. Bi-conditional proposition is also called material equivalence. The symbol called the tribar, to stand for material equivalence. The truth table for material equivalence is as follows: P Q P Q T T T T F F F T F F F T SYMBOLIC LOGIC AND INFORMATICS Page 24

25 MODULE 3 STATEMENT FORMS AND ARGUMENT FORMS For model questions, see the Question Bank. 10. Explain tautologous statement form. PART - A - Multiple-choice questions PART - B - Short answer questions A sentence is a tautology if the column under its main connective is True on every row of a complete truth table. Now consider the statement - It is raining or it is not raining, which is symbolized, as p v ~ p The truth table for p v ~ p is represented as follows: P ~ p p v ~ p T F T F T T Since we get only T in every row, this proposition is tautology. 11. Explain contradictory statement form. A sentence is a contradictory if the column under its main connective is False on every row of a complete truth table. Now consider: It is raining and it is not raining which is symbolized as p. ~ p The truth table for p v ~ p is represented as follows: P ~ p p ~ p T F F F T F Since we get only F in every row, the given proposition is contradictory. 12. Explain contingent statements. A sentence is contingent if it is neither a tautology nor a contradiction; i.e. if it is T on at least one row and F on at least one row. Now consider the statement: If it is raining then the roads are wet which is symbolized as P Q. The truth table for implication is as follows: SYMBOLIC LOGIC AND INFORMATICS Page 25

26 P Q P Q T T T T F F F T T F F T Since we get at least one T and one F in the rows, the given proposition is contingent. 13. Define argument form. An argument form can be defined as an array of symbols containing statement variables but no statements, such that when statements are substituted for statement variables-the same statement being substituted for the same statement variable throughout the result is an argument. An argument form is a group of sentence forms such that all its substitution instances are arguments. For example, all substitution instances of the form are arguments, and hence that form is an argument form. P Q P / Q PART - C - Paragraph answer questions 1. Explain the differences between argument and argument form. An argument is a set of sentences, one of which (the conclusion) is claimed to be supported by the others (the premises). Argument form is the logical st ructure of an argument. An argument can be proved invalid by constructing another argument of the same form with true premises and false conclusion. To prove the invalidity of an argument, it is sufficient to construct another argument of the same form with true premises and false conclusion. An argument form can be defined as an array of symbols containing statement variables but no statements, such that when statements are substituted for statement variables-the same statement being substituted for the same statement variable throughout the result is an argument. An argument form is a group of sentence forms such that all its substitution instances are arguments. For example, all substitution instances of the form P Q P / Q are arguments, and hence that form is an argument form. The order of the premises in an argument is irrelevant. Thus, P Q P P / Q and P Q / Q both can be thought of as substitution instances of the preceding form. Every valid argument is a substitution instance of at least one valid form. An invalid argument cannot be a substitution instance of a valid argument form. 2. Distinguish between validity and invalidity. SYMBOLIC LOGIC AND INFORMATICS Page 26

27 Truth and falsehood characterize propositions or statements. Arguments, however, are not considered as true or false but as valid or invalid. There is a connection between the validity or invalidity of an argument and the truth or falsehood of its premises and conclusion. An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. In the case of a valid argument, it is impossible for the premises to be true and at the same time the conclusion false. Validity is not about the actual truth or falsity of the sentences in the argument but instead, it is about the form of the argument. 3. Distinguish between tautology and contradiction. A sentence is a tautology if the column under its main connective is True on every row of a complete truth table. Now consider the statement - It is raining or it is not raining, which is symbolized as p v ~ p. The truth table for p v ~ p is represented as follows: P ~ p p v ~ p T F T F T T Since we get only T in every row, this proposition is tautology. A sentence is a Contradictory if the column under its main connective is False on every row of a complete truth table. Now consider: it is raining and it is not raining which is symbolized as p. ~ p The truth table for p v ~ p is represented as follows: P ~ p p ~ p T F F F T F Since we get only F in every row, this proposition is contradictory. PART - D - Essay questions 1. Explain tautology, contradiction and contingent statement forms. Construct truth table to find out which of the following compound statements are tautology, contradiction and contingent. a. (P Q) v ~ Q b. (P Q) ~Q c. (P Q) ~ (P Q) SYMBOLIC LOGIC AND INFORMATICS Page 27

28 Ans: In the case of compound statement, some will be contingent propositions, some will be tautologies, which are always true, and some will be contradictions, which are always false. We determine whether a given proposition is tautology, contradiction or contingent by constructing the truth tables. a. Tautology: A sentence is a tautology if the column under its main connective is True on every row of a complete truth table. Now consider: It is raining or it is not raining which is symbolized as p ~ p The truth table for p v ~ p is represented as follows: P ~ p p v ~ p T F T F T T Since we get only T in every row, this proposition is tautology. b. Contradictory: A sentence is a contradictory if the column under its main connective is False on every row of a complete truth table. Now consider: It is raining and it is not raining, which is symbolized as p ~ p The truth table for p v ~ p is represented as follows: P ~ p p ~ p T F F F T F Since we get only F in every row, this proposition is contradictory. c. Contingent: A sentence is contingent if it is neither a tautology nor a contradiction; i.e. if it is T on at least one row and F on at least one row. Now consider the statement: If it is raining then the roads are wet, which is symbolized as P Q. The truth table for implication is as follows: P Q P Q T T T T F F F T T F F T SYMBOLIC LOGIC AND INFORMATICS Page 28

29 Since we get at least one T and one F in the rows, this proposition is contingent. The division of sentences into tautologies, contradiction and contingent sentences is of fundamental importance. There is an important relationship between tautologies, contradictions, and valid arguments. To every valid argument, there corresponds a toutologous conditional sentence whose antecedent is the conjunction of the premises and whose consequent is the conclusion. The truth values of all tautologies and contradictions can be determine by logic alone, without appeal to experience or to any kind of empirical test, although this is not the case for contingent sentences. Thus, the division into tautologies, contradiction and contingent sentences is permitted to basic philosophical questions about the way in which knowledge can be acquired. Truth table for (P Q) ~ Q P Q ~ Q (P Q) (P Q) v ~ Q T T F T T T F T F T F T F T T F F T T T Since we get only T in every row, (P Q) v ~ Q is tautology. a. Truth table for (P Q) ~ Q P Q ~ Q (P Q) (P Q) ~ Q T T F T F T F T F F F T F T F F F T T T Since we get both T and F, (P Q) ~ Q is contingent. b. Truth table for (P Q) ~ (P Q) P Q (P Q) ~ (P Q) (P Q) ~ (P Q) T T T F F T F F T F F T T F F F F T F F Since we get only F in every row, (P Q) ~ (P Q) is contradiction. 2. Distinguish between validity and invalidity. SYMBOLIC LOGIC AND INFORMATICS Page 29

30 Truth and falsehood characterize proposition or statements. Arguments, however, are not properly characterized as being either true or false but as valid or invalid. There is a connection between the validity or invalidity of an argument and the truth or falsehood of its premises and conclusion. An argument is valid if and only if it is impossible for the premises to be true and the conclusion false. The crucial thing about a valid argument is that it is impossible for the premises to be true at the same time that the conclusion is false. The important thing to remember is that validity is not about the actual truth or falsity of the sentences in the argument. Instead, it is about the form of the argument. An argument is deductively valid if and only if it is impossible for the premises to be true and the conclusion false. The crucial thing about a valid argument is that it is impossible for the premises to be true at the same time that the conclusion is false. Consider this example: Oranges are either fruits or musical instruments. Oranges are not fruits. Therefore, oranges are musical instruments. The conclusion of this argument is ridiculous. Nevertheless, it follows validly from the premises. This is a valid argument. If both premises were true, then the conclusion would necessarily be true. This shows that a deductively valid argument does not need to have true premises or a true conclusion. Conversely, having true premises and a true conclusion is not enough to make an argument valid. Consider this example: London is in England. Paris is in France. Therefore, Beijing is in China. The premises and conclusion of this argument are, in fact, all true. This is a terrible argument, however, because the premises have nothing to do with the conclusion. Imagine what would happen if Beijing declared independence from the rest of China. Then the conclusion would be false, even though the premises would both still be true. Thus, it is logically possible for the premises of this argument to be true and the conclusion false. The argument is invalid. The important thing to remember is that validity is not about the actual truth or falsity of the sentences in the argument. Instead, it is about the form of the argument: The truth of the premises is incompatible with the falsity of the conclusion. 3. Distinguish between statements and statement forms. SYMBOLIC LOGIC AND INFORMATICS Page 30

31 A statement form is any sequence of symbols containing statement variables but no statements, such that when statements are substituted for the statement variables-the same statement being substituted for the same statement variable throughout- the result is a statement. Thus, ~p is called a negation form or denial form, p v q is a statement form called disjunctive statement form, p. q is called conjunctive statement form and p Ͻ q is conditional statement form. Any statement of a certain form is said to be a substitution instance of that statement form. The specific form of a given statement is defined as that statement form from which the statement results by substituting a different simple statement for each different statement variable. For example, p Ͻ q is the specific form of the statement A Ͻ B. Tautologous, Contradictory, and Contingent statement forms: We determine whether a given proposition is tautology, contradictory or contingent by looking at the truth tables. d. Tautology: A statement is a tautology if the column under its main connective is True on every row of a complete truth table. Now consider the statement - it is raining or it is not raining, which is symbolized as p v ~ p The truth table for p v ~ p is represented as follows: P ~ p p v ~ p T F T F T T Since we get only T in every row, this statement is tautology. e. Contradictory: A statement is a contradictory if the column under its main connective is False on every row of a complete truth table. Now consider: it is raining and it is not raining which is symbolized as p. ~ p The truth table for p v ~ p is represented as follows: P ~ p p. ~ p T F F F T F SYMBOLIC LOGIC AND INFORMATICS Page 31

32 Since we get only F in every row, this statement is contradictory. f. Contingent: A statement is contingent if it is neither a tautology nor a contradiction; i.e. if it is T on at least one row and F on at least one row. Now consider the statement: if it is raining then the roads are wet which is symbolized as P Ͻ Q. The truth table for implication is as follows: P Q P Ͻ Q T T T T F F F T T F F T Since we get at least one T and one F in the rows, this statement is contingent. SYMBOLIC LOGIC AND INFORMATICS Page 32

33 MODULE 4 FORMAL PROOF OF VALIDITY For model questions, see the Question Bank. PART - A - Multiple-choice questions PART - B - Short answer questions 1. Define formal proof of validity. If an argument contains many component statements, it is difficult to use truth table to test their validity. A more efficient method of establishing the validity of an argument is to deduce their conclusion from their premise by a sequence of shorter elementary arguments that are known to be valid. There are nine rules of inference, which help us to construct the formal proof of validity. In formal proof of validity, some rules are given and based on this rule the conclusion is derived. It starts with certain given statements, and with the help of certain self-evident rules, we deduce the conclusion. This method is called deductive method. Thus, in the decision procedure of the formal proof of validity, conclusion is drawn by applying the nine Rules of inference. 2. Define Modus ponens and give its symbolic form. Modus ponens is a form of hypothetical syllogism in which the minor premise affirms the antecedent and the conclusion affirms the consequent. Example: If one is a Gandhian, then she is a vegetarian. X is a Gandhian. X is a vegetarian p q p q 3. Define Modus Tollens and give its symbolic form. Modus Tollens is the rule of inference, which means denying the consequent and hence denying the antecedent. The symbolic form is p q ~q ~p 4. Define conjunction and give its symbolic form. In the rule of inference called conjunction, the conclusion is formed by joining all premises together. The symbolic form is SYMBOLIC LOGIC AND INFORMATICS Page 33

34 p q p q 5. Define simplification and give its symbolic form. Simplification is the opposite rule of conjunction. Here the first component of the conjunctive premise is inferred as the conclusion. The symbolic form is p q p 6. Define Addition and give its symbolic form. According to this rule of inference, we can add any number of variables to the given premise by disjunction. The symbolic form is p p v q 7. Define Absorption and give its symbolic form. According to this rule, if p implies q it also implies p and q because any proposition implies itself. The symbolic form is p q p (p q) 8. Present the symbolic form of Modus Ponens, Modus Tollens and Constructive Dilemma. a) Modus Ponens (M.P) p q p q c) Constructive Dilemma (C. D.) (p q) (r s) p v r q v s b) Modus Tollens (M.T) p q ~q ~p 9. Construct the formal proof of validity of the following: A B B C C D ~D/ ~A 1. A B 2. B C SYMBOLIC LOGIC AND INFORMATICS Page 34

35 3. C D 4. ~D / ~A 5. B D 2,3H.S 6. ~B 5,4 M.T 7. ~A 1,6 M.T 10. State the justification for each line that is not a premise. 1. A B 2. (A v C) D/ A D 3. A 4. A v C 5. D 6. A D 1. A B 2. (A v C) D/ A D 3. A 1,Simplification 4. A v C 3,Addition 5. D 2,4 Modus ponens 6. A D 3,5 conjunction 11. Write a note on Hypothetical Syllogism and its symbolic form. In pure hypothetical syllogism, all the propositions are hypothetical propositions. For example, If john catches the train then he will meet his family. If he meets his family then the company will appoint new person. Therefore, if john catches the train then the company will appoint new person. The rules of pure hypothetical syllogism are as follows: 1) Both of the premises should have one common categorical proposition. 2) This common proposition is the antecedent in one premise and consequent in other premise. 3) The conclusion should not have this common term, but instead it should contain the antecedent of one premise as antecedent (other than the common term) and consequent other premise as consequent (other than the common term) Symbolic form p q q r p r SYMBOLIC LOGIC AND INFORMATICS Page 35

36 12. Construct the formal proof validity of the following arguments. A. If it rains in time, there will be good crops. If there are good crops, then prices of essential commodities will not increase. It rains in time. Therefore, the prices of essential commodities will not increase. 1. R C 2. C ~I 3. R / ~I Answer 1. R C 2. C ~I 3. R / ~I 4. C 1,3 M.P 5. ~I 2, 4 M.P B. If the students protest hike in fees then either the college will withdraw extra facilities or the government will have to spend more. The students will protest hike in fees. The college will not withdraw extra facilities. Therefore, the government will have to spend more. 1. S (F v G) 2. S 3. ~F / G 4. F v G 1,2 M.P 5. G 4,3 D.S 13. State the rule of inference for the following arguments. 1. (A ~B) (~C D) A ~B Ans. Simplification 2. E ~F (E ~F) v (~G H) Ans. Addition 3. (F ~G) (~H v ~I) F ~G ~H v ~I Ans. Modus Ponens SYMBOLIC LOGIC AND INFORMATICS Page 36

37 PART - C - Paragraph answer questions 1. Describe constructive dilemma and give its symbolic form. Every dilemma has two conditional propositions as its major premises. In constructive dilemma, the major premise has two different antecedents, both leading to different consequents. E.g. If the salaries are increased, the economy is adversely affected and If the salaries are not increased, there will be wide spread agitation. Either the salaries are increased or not. Either the economy is adversely affected or there are wide spread agitation. If A is B, C is D and E is F, G is H Either A is B or E is F Either C is D or G is H This is constructive because disjunctive minor premise affirms the antecedents. The Symbolic form (p q) (r s) p v r q v s 2. Construct the formal proof of validity of the following argument. N M M D M P ~P N v M / D Ans. 1. N M 2. M D 3. M P 4. ~P 5. N v M / D 6. ~M 3,4 M.T 7. ~N 1,6 M.T 8. M 5,7 D.S SYMBOLIC LOGIC AND INFORMATICS Page 37

38 9. D 2,8 M.P 3. Write a note on Disjunctive Syllogism. Disjunctive syllogism is a mixed syllogism in which major premise is a disjunctive proposition (Alternatives are joined by either -- or), minor premise and conclusion are categorical propositions. Rules E.g. Ram is either mad or drunk. Ram is not mad. Ram is drunk. 1) First premise is disjunctive proposition. 2) Second premise is negation of one of the disjuncts of major premise. 3) Conclusion is the remaining disjunct or disjuncts. A valid disjunctive syllogism can be one of the following types: 1) Either p or q p v q Not p ~p Therefore, q q 2) Either p or q p v q Not q ~q Therefore, p p 4. State the justification for the given proof of validity. 1. F v (G v H) 2. (G I) (H I) 3. (I v J) (F v H) 4. ~F / H 5. G v H 6. I v J 7. F v H 8. H Ans. 1. F v (G v H) SYMBOLIC LOGIC AND INFORMATICS Page 38

39 2. (G I) (H Ɔ I) 3. (I v J) (F v H) 4. ~F / H 5. G v H 1, 4 D.S 6. I v J 2,5C.D 7. F v H 3, 6 M.P 8. H 4, 7 D.S 5. Construct the formal validity of the following argument. P ~q ~q r r s (p s) u / p u Ans: 1. P ~q 2. ~q r 3. r s 4. (p s) u / p u 5. p r 1,2,H.S 6. p s 5,3H.S 7. p (p s) 6 Abs. 8. p u 7,4 H.S 6. Briefly explain Modus ponens and Modus tollens and give its symbolic form. Modus Ponens (Constructive hypothetical syllogism) It is a form of hypothetical syllogism in which the minor premise affirms the antecedent and the conclusion affirms the consequent. Example: If a man is a Gandhian, then he is a vegetarian. X is a Gandhian. X is a vegetarian. Symbolic form P p q Modus Tollens (Destructive Hypothetical Syllogism) It is a form of hypothetical syllogism in which the minor premise denies the consequent and the conclusion denies the antecedent of major premise. Example: If he is a thief, he will hide the goods. SYMBOLIC LOGIC AND INFORMATICS Page 39

40 Symbolic form p q ~q ~p He has not hidden the goods. He is not a thief. 7. State the rules of inference by which the conclusion follows from premise or premises. 1. A v (B D) 2. ~C (D E) 3. A C 4. ~C / B E Answer 1. A v (B D) 2. ~C (D E) 3. A C 4. ~C / B E 5. ~A 3, 4 M.T 6. B D 1, 5 D.S 7. D E 2, 4 M.P 8. B E 6, 7 H.S 8. Construct the formal proof of validity for the following Argument. A B C D A C / B D 1. A B 2. C D 3. A C / B D 4. A 3 Simp. 5. B 1,4 M.P 6. A D 1,2 H.S 7. D 4, 6 M.P 8. B D 5, 7 Conj. 9. Symbolize the given argument using the symbols given in brackets and construct the formal proof of validity for the following. If a tenth planet exists, then its orbit is perpendicular to that of other planets. Either the tenth planet is responsible for the death of the dinosaurs or its orbit is not perpendicular to SYMBOLIC LOGIC AND INFORMATICS Page 40

41 that of other planets. A tenth planet is not responsible for the death of the dinosaurs. Therefore, a tenth planet does not exist. (E, P, R) Symbolic form: E P R v ~P ~R / ~E Formal proof: 1. E P 2. R v ~P 3. ~R / ~E 4. ~P 2, 3 D.S 5. ~E 1, 4 M.T 10. Write a note on any two of the following and present their symbolic forms. a)hypothetical syllogism b) Formal proof of validity c) Modus ponens (Prepare the answers by collecting and arranging the relevant answers from Part B and C) Part - D - Essay questions 1. Define formal proof of validity and present the symbolic form of nine elementary valid argument forms. (Prepare the essay by collecting and arranging the relevant answers from Part B and C) 2. Present the nine rules of inference and construct the formal proof of validity for the given argument. (W v X) Y (W v X) Z ~Y / Z (Prepare the first part of the essay by collecting and arranging the relevant answers from Part B and C) Answer to the second part: 1. (W v X) Y 2. (W v X) v Z 3. ~Y / Z 4. ~ (W v X) 1, 3 M.T 5. Z 2, 4 D.S 3. Write a note on any two of the following and give its symbolic form. SYMBOLIC LOGIC AND INFORMATICS Page 41

42 a. Constructive Dilemma b. Hypothetical syllogism c. Modus Ponens and Modus Tollens d. Disjunctive syllogism (Prepare the essay by collecting and arranging the relevant answers from Part B and C) 3. Define formal proof of validity and construct the formal proof of validity for the following argument using the abbreviations suggested. If either algebra is required or geometry is required, then all students will study mathematics. Algebra is required and Trigonometry is required. Therefore, all students will study Mathematics. ( A: Algebra, G: Geometry, T: Trigonometry, S: study, M: Mathematics) (Prepare the first part of the essay by collecting and arranging the relevant answers from Part B and C). Answer to the second part: 1. (A v G) M 2. A T / M 3. A 2, Simp. 4. A v G 3, Add. 5. M 1, 4 M.P SYMBOLIC LOGIC AND INFORMATICS Page 42

43 MODULE 5 INFORMATICS (The informatics portions in this module are prepared on the basis of the Textbook Informatics: Technology in Action authored by Alan Evans et al.) PART - A - Multiple-choice questions For model questions, see the Question Bank. PART - B - Short answer questions 1. Define informatics. Informatics is the science of computer information system. As an academic field, it involves the practice of information processing. As a combination of information and automatic, informatics is also defined as the science of automating information interactions. Informatics includes different fields like Health informatics, Bio- informatics, Business informatics and Engineering informatics. 2. Define Data. In computer terms, data is a representation of a fact or idea. Data can be a number, a word, a picture, or even a recorded sound. For example, the number and the names Derek and Washington are pieces of data. 3. Distinguish between data and information. In computer terms, data is a representation of a fact or idea. Data can be a number, a word, a picture, or even a recorded sound. For example, numbers and the names are pieces of data. Data becomes information when organized in a meaningful way. For example, when a set of ordered numbers represent the telephone number of a person it is an information. 3. Explain the term privacy. Privacy refers to the right of a person to maintain certain facts to oneself without the knowledge of others. It is a basic human right like the right to be treated with dignity. Unlimited privacy is the right to be left alone to do as one pleases. The idea of privacy is often associated with hiding something. In computer terms privacy is the right to protect the digital data and information without giving access to others. 4. Describe Cyber addiction. Cyber addiction is the abnormal tendency to excessive use of computers and internet. It is an addiction that affects the routine life of an individual who becomes too much dependent on computer and internet. Cyber addiction is just like any other form of addiction where there is a strong craving towards internet surfing. Cyber addiction appears in different forms like computer addiction, cyber relational addiction and net gaming addiction. 5. What is meant by information overload? SYMBOLIC LOGIC AND INFORMATICS Page 43

44 Information overload refers to the addiction towards unlimited information available on the internet. The addict in this case has a craving for searching, reading and storing information of his interest on the internet. It often results in stress and anxiety related disorders. The term information overload was first used by the great futurist and writer Alvin Toffler in his book Future Shock. Toffler regards information overload as a psychological disorder caused by an abundance of information availability. 6. Explain the notions of Computer addiction and Cyber relational addiction. Computer addiction may or may not include addiction towards the internet. It particularly includes addiction towards playing computer games. Cyber relational addiction refers to the addiction towards socializing through the internet. The addict in this case finds a craving for creating online friends through social networking sites; thus often neglecting the real social life. 7. Explain the role of Cyber laws in the context of Information explosion. Cyber laws are a set of legal provisions to regulate cyber activities including internet use. The unusual increase in the number of internet users is followed by an increase in the number cyber crimes. Hence, all national governments are forced to frame rigid cyber laws. They include not only the laws to prevent cyber crimes but also the intellectual property right rules. In India, cyber laws have been defined under the IT Act Present the diagrammatic representation of NOT and OR gates. NOT Gate OR Gate 9. Present the diagrammatic representation and truth table for AND gate. Diagram SYMBOLIC LOGIC AND INFORMATICS Page 44

45 Truth table PART - C - Paragraph answer questions 1. What is the difference between data and information? In ordinary language, the terms data and information are used interchangeably. However, in computer terms, the distinction between data and information is very important. In computer terms, data is a representation of a fact or idea. Data can be a number, a word, a picture, or even a recorded sound. For example, numbers and the names are pieces of data. Data becomes information when organized in a meaningful way. For example, when a set of ordered numbers represent the telephone number of a person it is information. Hence, data become useful when it assumes the status of information. Computers are very good at processing data into information. For example, the necessary personal data about a citizen become specific information when it is processed into the ADHAAR Card. This organized output of data on your ID card is a set of useful information. 2. How do computers process data into information? Computers work with a binary language that consists of just two digits: 0 and 1. All data on a computer is stored in the combinations of 0s and 1s. Each 0 and 1 is a binary digit, or bit for short. Eight binary digits or bits combine to create one byte. In computers, each letter of alphabet, each number, and each special character is a unique combination of eight bits, or a string of eight 0s and 1s. For example, in computer language, the letter K is represented as This equals eight bits, or one byte. A kilobyte (KB) is approximately 1000bytes, a megabyte (MB) is about a million bytes, SYMBOLIC LOGIC AND INFORMATICS Page 45

46 and a gigabyte (GB) is about a billion bytes. In the computer world, the storage needs are so high today that some computers can store more than one quadrillion bytes, that is, a petabyte of data. In a computer, bits and bytes represent the data and information it inputs and outputs. All data processing is based on this special digital language used in a computer. 3. What is ethical computing? We have many examples of the unethical use of computers. There are stories about cyber crimes coming out in media every day. Unexpected virus attacks and illegal sharing of copyright protected materials are not rare today. However, it is not easy to define what constitutes ethical behaviour while using a computer. Ethics is a system of moral principles, rules, and accepted standards of conduct. So what are the accepted standards of conduct when using computers? The Computer Ethics Institute developed the Ten Commandments of Computer Ethics, which may guide our ethical standards in the cyber world. These Ethical Computing Guidelines are stated below: 1. Avoiding causing harm to others when using computers. 2. Do not interfere with other people s efforts at accomplishing work with computers. 3. Resist the temptation to snoop in other people s computer files. 4. Do not use computers to commit theft. 5. Agree not to use computers to promote lies. 6. Do not use software (or make illegal copies for others) without paying the creator for it. 7. Avoid using other people s computer resources without appropriate authorization or proper compensation. 8. Do not claim other people s intellectual output as your own. 9. Consider the social consequences of the products of your computer labour. 10. Only use computers in way that show consideration and respect for others. 4. Summarize the issue of privacy in the cyber world. Privacy refers to the right of a person to maintain certain facts to oneself without the knowledge of others. It is a basic human right like the right to be treated with dignity. Unlimited privacy is the right to be left alone to do as one pleases. The idea of privacy is often associated with hiding something. In computer terms, privacy is the right to SYMBOLIC LOGIC AND INFORMATICS Page 46

47 protect the digital data and information without giving access to others. It is indeed necessary in the present day world of digitalized services in all areas like communication, banking and marketing. We are using debit and credit cards for purchasing and bank transactions. is the common means to correspondence. In such cases, it is necessary to maintain privacy by preventing the chances of identity theft and phishing. Computer experts advise us to change our behaviour to protect privacy. It is necessary to stop giving personal information to unknown internet queries. We should take proper care to keep our cyber identity like passwords, phone numbers and secret codes. Governments are framing cyber laws that include the rules to protect our privacy in the cyber world. 5. Discuss the for and against arguments of the problem of privacy. Arguments for privacy: The advocates for protecting privacy argue that the right to privacy is a basic human right and it should be ensured in the digital world also. The main reasons they give are the following: 1. If I am not doing anything wrong, then you have no reason to watch me. 2. If the government is collecting information by watching citizens, it might misuse or lose control of the data. 3. By allowing the government to determine what behaviours are right and wrong, we open ourselves to uncertainty because the government may arbitrarily change the definition of acceptable behaviours. 4. Requiring national ID cards is reminiscent of the former Nazi or Soviet regimes. 5. Implementing privacy controls (such as national ID cards) is extremely expensive and a waste of taxpayer funds. Arguments against privacy: Advocates for stronger monitoring of private citizens emphasize national security concerns like the prevention of terrorist activities. Personal inconvenience is just the price for social security and peace. The main reasons they give are the following: 1. If you are not doing anything wrong, you need not hide anything. 2. Electronic identification documents are essential in the digital world to exchange information and to detect suspected terrorists. 3. Laws protect citizens from the abuse and misuse of government officials who are involved in monitoring activities. SYMBOLIC LOGIC AND INFORMATICS Page 47

48 4. It is not possible to put a price on freedom or security and hence projects like a national ID system are worth the cost of implementation. 6. What is cyber addiction and explain the various terms related to cyber addiction. Cyber addiction refers to the tendency to too much use of the computer and internet to the extent of affecting the routine life of an individual. One who becomes too much dependent on computer and internet is called a cyber addict. Cyber addiction is just like any other form of addiction such as that of television, alcohol, gambling, drugs etc. Cyber addiction is specified by many other terms, like computer addiction, cyber relational addiction and net gaming. Computer addiction: It may or may not include addiction towards the internet. It particularly includes addiction towards playing computer games. Cyber relational addiction: It refers to the addiction towards socialising though the internet. The addict in this case finds a craving for creating online friends through social networking sites; thus often neglecting the real social life. Net gaming: As the name suggests, the addict in this case finds a strong craving towards playing online games. The addict particularly finds great sense of triumph in beating other online gamers. 7. Analyze the issues related with Information overload. Information overload refers to the addiction towards unlimited information available on the internet. The addict in this case has a craving for searching, reading and storing information of his interest on the internet. It often results in stress and anxiety related disorders. The great futurist writer Alvin Toffler in his book Future Shock first used the term information overload. Toffler regards information overload as a psychological disorder caused by an abundance of information availability. The amount of information on the internet has led to an information explosion. More and more number of internet users is becoming addicts of information overload and they gradually enter a virtual world of websites, s, blogs, reviews, messengers, social networking sites etc. Indifference to day-to-day affairs, increasing anxiety and stress are symptoms of this addiction. In order to protect oneself from information overload it is necessary to access the information in a systematic manner just to meet the necessary requirements. 8. Present the symbols for AND, OR and NOT gates. SYMBOLIC LOGIC AND INFORMATICS Page 48

49 AND OR NOT 9. Present the truth tables for OR and NOT gates. OR Gate NOT Gate PART D - Essay questions 1. Define informatics and bring out of the relationship and differences between data, information and knowledge in the digital world. Informatics is the science of computer information system. As an academic field, it involves the practice of information processing. As a combinationn of information and automatic, informatics is also defined as the sciencee of automating information interactions. Informatics includes different fields like Health informatics, Bio- informatics, Business informatics and Engineering informatics. We are living in a world of digitalization and information overload. Computers and accessories have become a part of our day-to-day life. Computers are basically data processing devices that may be used in a variety of ways. In ordinary language, we often use the terms data and information interchangeably. However, in the world of computers, the distinction between data and information is not that simple. In computer terms, data is a representation of a fact or idea. Data can be a number, a word, a picture, or even a recorded sound. For example, numbers and names are pieces of data. Data becomes information when organized in a meaningful way. For example, when a set of ordered numbers represent the telephone number of a person it is information. The main functions of a computer as a data processing machine are the following: i) Collecting and storing data input by the user. ii) Processing that data into information. SYMBOLIC LOGIC AND INFORMATICS Page 49

50 iii) Outputs data and information. iv) Stores data and information. These functions in different combinations make a computer the fastest and the most efficient companion in all fields of human life like communication, education, medicine, commerce etc. We have seen that data is a representation of a fact or idea. For example, the number 203 and the name Sofia are pieces of data. Information is data that has been organised or presented in a meaningful fashion. When we know that 203 is the ID Card number of Sofia the data mentioned earlier suddenly becomes useful - that is, information. Knowledge is defined as information, understanding and skills learned through education or experience. Information is identified as knowledge when it is classified into a particular field such as science, philosophy or medicine. Moreover, knowledge may be theoretical or practical. A knowledgeable person is of course well informed about a specific field of study like biology or mathematics or about the stream of life in this world. How do computers interact with data and information? Computers are very good at processing data into information. When you first arrived on campus, you probably were directed to a place where you could get an ID card. You most likely provided a clerk with personal data that was entered into a computer. The clerk then took your picture with a digital camera. This information was then processed appropriately so that it could be printed on your ID card. This organized output of data on your ID card is useful information. Finally, the information was probably stored as a digital data on the computer for later use. Computers work with a binary language that consists of just two digits: 0 and 1. All data on a computer is stored in the combinations of 0s and 1s. Each 0 and 1 is a binary digit, or bit for short. Eight binary digits or bits combine to create one byte. In computers, each letter of alphabet, each number, and each special character is a unique combination of eight bits, or a string of eight 0s and 1s. For example, in computer language, the letter K is represented as This equals eight bits, or one byte. A kilobyte (KB) is approximately 1000bytes, a megabyte (MB) is about a million bytes, and a gigabyte (GB) is about a billion bytes. In the computer world, the storage needs are so high today that some computers can store more than one quadrillion bytes, that is, a petabyte of data. In a computer, bits and bytes represent the data and information it inputs and outputs. All data processing is based on this special digital language used in a computer. 2. Briefly describe the ethical issues related with cyber world. We are living in a world of digitalization and information overload. Computers and accessories have become a part of our day-to-day life. Informatics is the science of computer information system. As an academic field, it involves the practice of SYMBOLIC LOGIC AND INFORMATICS Page 50

51 information processing. Informatics includes different fields like Health informatics, Bio- informatics, Business informatics and Engineering informatics. There is a vast range of ethical issues related to the cyber world. Issues of privacy, cyber addiction and information overload are considered as the most important among them. Cyber ethics is an emerging area of ethics dealing with the good and bad in human relation to the digital devices and the acquisition, storage and exchange of data and information through such means. The terms like privacy, identity theft etc have become the concern of computer literate people. Cyber crimes like phishing and hacking are increasing day by day. Privacy: Privacy refers to the right of a person to maintain certain facts to oneself without the knowledge of others. It is a basic human right like the right to be treated with dignity. Unlimited privacy is the right to be left alone to do as one pleases. The idea of privacy is often associated with hiding something. In computer terms, privacy is the right to protect the digital data and information without giving access to others. It is indeed necessary in the present day world of digitalized services in all areas like communication, banking and marketing. We are using debit and credit cards for purchasing and bank transactions. is the common means to correspondence. In such cases, it is necessary to maintain privacy by preventing the chances of identity theft and phishing. As the use of digital devices is increasing, the number of unlawful methods to break into personal computers is also increasing. Computer experts advise us to change our behaviour to protect privacy. It is necessary to stop giving personal information to unknown internet queries. We should take proper care to keep our cyber identity like passwords, phone numbers and secret codes. Governments are framing cyber laws that include the rules to protect our privacy in the cyber world. The advocates for protecting privacy argue that the right to privacy is a basic human right and it should be ensured in the digital world also. They point out the chances of governments misusing the data of citizens for the interests of the state. Making national ID cards compulsory is a waste of public money. The main argument for privacy is that if I am not doing anything wrong, then you have no reason to watch me. Advocates for stronger monitoring of private citizens emphasize national security concerns like the prevention of terrorist activities. Personal inconvenience is just the price for social security and peace. Laws protect citizens from the abuse and misuse of government officials who are involved in monitoring activities. Cyber addiction Cyber addiction refers to the tendency to too much use of the computer and internet to the extent of affecting the routine life of an individual. One who becomes too much dependent on computer and internet is called a cyber addict. Cyber addiction is just like any other form of addiction such as that of television, alcohol, gambling, drugs etc. Cyber addiction SYMBOLIC LOGIC AND INFORMATICS Page 51

52 is specified by many other terms, like computer addiction, cyber relational addiction and net gaming. Computer addiction: It may or may not include addiction towards the internet. It particularly includes addiction towards playing computer games. Cyber relational addiction: It refers to the addiction towards socializing though the internet. The addict in this case finds a craving for creating online friends through social networking sites; thus often neglecting the real social life. Net gaming: As the name suggests, the addict in this case finds a strong craving towards playing online games. The addict particularly finds great sense of triumph in beating other online gamers. Information overload Information overload refers to the addiction towards unlimited information available on the internet. The addict in this case has a craving for searching, reading and storing information of his interest on the internet. It often results in stress and anxiety related disorders. The great futurist writer Alvin Toffler in his book Future Shock first used the term information overload. Toffler regards information overload as a psychological disorder caused by an abundance of information availability. The amount of information on the internet has led to an information explosion. More and more number of internet users is becoming addicts of information overload and they gradually enter a virtual world of websites, s, blogs, reviews, messengers, social networking sites etc. Indifference to day-to-day affairs and increasing anxiety and stress mark the addiction to information overload. In order to protect oneself from information overload it is necessary to access the information in a systematic manner just to meet the necessary requirements. Like any other technological achievement, digital technology also has the chances of both use and misuse. Hence, Cyber ethics is the need of the day. It is necessary for cyber experts and rulers to join hands to define the crimes and decide the punishments in the cyber world. 3. Define logical gate and present the symbols and truth tables for AND, NOT and OR gates.* Logic gates are the basic building blocks of any digital system. They process signals, which represent the binaries of true/false. Normally, the positive supply voltage +5V represent true and 0V represents false. A logic gate has one or more input and only one output. The input-output relationship is based on a definite logic and hence the name logic gate. The basic logic gates are AND, NOT and OR. There are also universal gates like NAND gate in which an AND gate is followed by a NOT gate and the NOT- OR operation called NOR gate. Combinational gates are X-OR gate and X-NOR gate. SYMBOLIC LOGIC AND INFORMATICS Page 52

53 AND Gate SYMBOLS NOT Gate OR Gate TRUTH TABLES AND Gate OR Gate SYMBOLIC LOGIC AND INFORMATICS Page 53