MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
|
|
- Charity Harrington
- 5 years ago
- Views:
Transcription
1 Worksheet 10. (Sec ) Please indicate the most suitable answer on blank near the right margin. Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the negation of the conditional statement. 1) If she can't take out the trash, I will. 1) A) She can take out the trash, and I can't. B) She can't take out the trash, and I won't. C) If she can take out the trash, I can't. D) She can't take out the trash, I can't. 2) If I get a high-paying job, then I can pay off all my bills. 2) A) I get a high-paying job and can pay off all my bills. B) I get a high-paying job and I cannot pay off all my bills. C) I don't get a high-paying job and can pay off all my bills. D) I don't get a high-paying job and cannot pay off all my bills. Use the De Morgan law that states: ~() is equivalent to ~ p to write an equivalent English statement for the statement. 3) It is not true that Boston and Russia are both states. 3) A) If Boston is a state, then Russia is not a state. B) Boston is not a state and Russia is not a state. C) It is true that Boston and Russia are both states. D) Boston is not a state or Russia is not a state. Use De Morgan's laws to write a negation of the statement. 4) She is not older than 21 and he is older than 21. 4) A) It is not true that she is older than 21 or he is not older than 21. B) She is older than 21 or he is not younger than 21. C) She is older than 21 or he is not older than 21. D) She is older than 21 but he is not older than 21. Use a truth table to determine whether the symbolic form of the argument is valid or invalid. 1
2 5) 5) p r ~ r q A) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) F T T F T F F T F B) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) T T F T F F T T F T F T F T F F T F T F F F F F T F F F T T F T F F T F F T F F T F T T F C) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) F T T F T F F T T F F F T T T T F T Symbolic argument is valid. 2
3 D) p q r p r () (p r) ~ r ~ r q [() (p r)] (~ r q) F T T F T F F T T 6) () (q r) 6) p r A) Valid B) Invalid SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Translate the argument into symbolic form. Then use a truth table to determine whether the argument is valid or invalid. (Ignore differences in past, present, and future tense.) 7) If it is July or August, then I am living at the beach 7) I am not living at the beach. It is neither July nor August. 3
4 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Write the passage in the form of an argument using the following simple statements: p: The "diamond" is a fake. q: Peter will be unhappy for weeks. The argument's conclusion should be: The diamond must not have been a fake. Determine if the argument is valid or invalid. 8) Peter bought a "diamond" from a street vendor. I was sure it was a fake and that it would make 8) Peter miserable for weeks. But I saw him a few days later. He had got the "diamond" appraised and looked quite happy... A) p The argument is invalid. C) The argument is invalid. B) D) The argument is valid. The argument is valid. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Draw a valid conclusion from the given premises. 9) If I work in the garden, my back gets sore. 9) If my back gets sore, I take a hot bath Therefore... 4
5 Translate the argument into symbolic form, then use the table below to determine whether the argument is valid or invalid. Indicate valid/invalid and identify the type of answer. VALID ARGUMENTS Direct Contrapositive p q INVALID ARGUMENTS Disjunctive ~ p q p Transitive q r ~ r Fallacy of the Converse q p Fallacy of the Inverse ~ p Misuse of Disjunctive p q Misuse of Transitive q r r p ~ r 10) If Fred studies hard, then he gets a good grade. 10) Fred got a good grade. He studies hard. 11) If he wants to come, he will say so. 11) If he says so, then he will come. If he comes, that means he wants to. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use an Euler diagram to determine whether the argument is valid or invalid. 12) All insects have six legs. 12) No spiders are insects. Therefore, no spiders have six legs. 13) Some people enjoy walking. 13) Some people enjoy swimming. Therefore, some people who enjoy walking enjoy swimming. 14) All soda pops are carbonated. 14) All diet colas are soda pops. Therefore, all diet colas are carbonated. 5
1) The set of the days of the week A) {Saturday, Sunday} B) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday}
Review for Exam 1 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. List the elements in the set. 1) The set of the days of the week 1) A) {Saturday,
More information2. The Logic of Compound Statements Summary. Aaron Tan August 2017
2. The Logic of Compound Statements Summary Aaron Tan 21 25 August 2017 1 2. The Logic of Compound Statements 2.1 Logical Form and Logical Equivalence Statements; Compound Statements; Statement Form (Propositional
More informationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MTH 164 Practice Exam 2 Spring 2008 Dr. Garcia-Puente Name Section MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide whether or not the following
More informationChapter 1: The Logic of Compound Statements. January 7, 2008
Chapter 1: The Logic of Compound Statements January 7, 2008 Outline 1 1.1 Logical Form and Logical Equivalence 2 1.2 Conditional Statements 3 1.3 Valid and Invalid Arguments Central notion of deductive
More informationProposition logic and argument. CISC2100, Spring 2017 X.Zhang
Proposition logic and argument CISC2100, Spring 2017 X.Zhang 1 Where are my glasses? I know the following statements are true. 1. If I was reading the newspaper in the kitchen, then my glasses are on the
More informationWhere are my glasses?
Proposition logic and argument CISC2100, Spring 2017 X.Zhang 1 Where are my glasses? I know the following statements are true. 1. If I was reading the newspaper in the kitchen, then my glasses are on the
More informationPSU MATH RELAYS LOGIC & SET THEORY 2017
PSU MATH RELAYS LOGIC & SET THEORY 2017 MULTIPLE CHOICE. There are 40 questions. Select the letter of the most appropriate answer and SHADE in the corresponding region of the answer sheet. If the correct
More informationTHE LOGIC OF COMPOUND STATEMENTS
CHAPTER 2 THE LOGIC OF COMPOUND STATEMENTS Copyright Cengage Learning. All rights reserved. SECTION 2.1 Logical Form and Logical Equivalence Copyright Cengage Learning. All rights reserved. Logical Form
More informationSection 3.1 Statements, Negations, and Quantified Statements
Section 3.1 Statements, Negations, and Quantified Statements Objectives 1. Identify English sentences that are statements. 2. Express statements using symbols. 3. Form the negation of a statement 4. Express
More informationDeMorgan s Laws and the Biconditional. Philosophy and Logic Sections 2.3, 2.4 ( Some difficult combinations )
DeMorgan s aws and the Biconditional Philosophy and ogic Sections 2.3, 2.4 ( Some difficult combinations ) Some difficult combinations Not both p and q = ~(p & q) We won t both sing and dance. A negation
More informationLogic Review Solutions
Logic Review Solutions 1. What is true concerning the validity of the argument below? (hint: Use a Venn diagram.) 1. All pesticides are harmful to the environment. 2. No fertilizer is a pesticide. Therefore,
More information1) A) 1 B) 2 C) 3 D) 2 3
MATH 100 -- EXAM 1 Millersville University, Fall 2007 Ron Umble, Instr. Name INSTRUCTIONS: Turn off and stow all cell phones and pagers. Calculators may be used, but cell phone may not be used as calculators.
More informationANALYSIS EXERCISE 1 SOLUTIONS
ANALYSIS EXERCISE 1 SOLUTIONS 1. (a) Let B The main course will be beef. F The main course will be fish. P The vegetable will be peas. C The vegetable will be corn. The logical form of the argument is
More informationMat 243 Exam 1 Review
OBJECTIVES (Review problems: on next page) 1.1 Distinguish between propositions and non-propositions. Know the truth tables (i.e., the definitions) of the logical operators,,,, and Write truth tables for
More informationCHAPTER 6 - THINKING ABOUT AND PRACTICING PROPOSITIONAL LOGIC
1 CHAPTER 6 - THINKING ABOUT AND PRACTICING PROPOSITIONAL LOGIC Here, you ll learn: what it means for a logic system to be finished some strategies for constructing proofs Congratulations! Our system of
More informationReview Test 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Review Test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the statement is true or false. 1) 4 {1, 2, 3,..., 15} A) True B)
More informationLOGIC CONNECTIVES. Students who have an ACT score of at least 30 OR a GPA of at least 3.5 can receive a college scholarship.
LOGIC In mathematical and everyday English language, we frequently use logic to express our thoughts verbally and in writing. We also use logic in numerous other areas such as computer coding, probability,
More informationLecture 2. Logic Compound Statements Conditional Statements Valid & Invalid Arguments Digital Logic Circuits. Reading (Epp s textbook)
Lecture 2 Logic Compound Statements Conditional Statements Valid & Invalid Arguments Digital Logic Circuits Reading (Epp s textbook) 2.1-2.4 1 Logic Logic is a system based on statements. A statement (or
More information3.2: Compound Statements and Connective Notes
3.2: Compound Statements and Connective Notes 1. Express compound statements in symbolic form. _Simple_ statements convey one idea with no connecting words. _Compound_ statements combine two or more simple
More informationCSC Discrete Math I, Spring Propositional Logic
CSC 125 - Discrete Math I, Spring 2017 Propositional Logic Propositions A proposition is a declarative sentence that is either true or false Propositional Variables A propositional variable (p, q, r, s,...)
More informationThe statement calculus and logic
Chapter 2 Contrariwise, continued Tweedledee, if it was so, it might be; and if it were so, it would be; but as it isn t, it ain t. That s logic. Lewis Carroll You will have encountered several languages
More informationCS100: DISCRETE STRUCTURES. Lecture 5: Logic (Ch1)
CS100: DISCREE SRUCURES Lecture 5: Logic (Ch1) Lecture Overview 2 Statement Logical Connectives Conjunction Disjunction Propositions Conditional Bio-conditional Converse Inverse Contrapositive Laws of
More informationWhat is Logic? Introduction to Logic. Simple Statements. Which one is statement?
What is Logic? Introduction to Logic Peter Lo Logic is the study of reasoning It is specifically concerned with whether reasoning is correct Logic is also known as Propositional Calculus CS218 Peter Lo
More informationOutline. Rules of Inferences Discrete Mathematics I MATH/COSC 1056E. Example: Existence of Superman. Outline
Outline s Discrete Mathematics I MATH/COSC 1056E Julien Dompierre Department of Mathematics and Computer Science Laurentian University Sudbury, August 6, 2008 Using to Build Arguments and Quantifiers Outline
More informationUnit I LOGIC AND PROOFS. B. Thilaka Applied Mathematics
Unit I LOGIC AND PROOFS B. Thilaka Applied Mathematics UNIT I LOGIC AND PROOFS Propositional Logic Propositional equivalences Predicates and Quantifiers Nested Quantifiers Rules of inference Introduction
More information5. Use a truth table to determine whether the two statements are equivalent. Let t be a tautology and c be a contradiction.
Statements Compounds and Truth Tables. Statements, Negations, Compounds, Conjunctions, Disjunctions, Truth Tables, Logical Equivalence, De Morgan s Law, Tautology, Contradictions, Proofs with Logical Equivalent
More informationCSCI Homework Set 1 Due: September 11, 2018 at the beginning of class
CSCI 3310 - Homework Set 1 Due: September 11, 2018 at the beginning of class ANSWERS Please write your name and student ID number clearly at the top of your homework. If you have multiple pages, please
More informationChapter 3: Logic. Diana Pell. A statement is a declarative sentence that is either true or false, but not both.
Chapter 3: Logic Diana Pell Section 3.1: Statements and Quantifiers A statement is a declarative sentence that is either true or false, but not both. Exercise 1. Decide which of the following are statements
More informationFUNDAMENTALS OF MATHEMATICS HANDOUT 1.3 DR. MCLOUGHLIN
021 McLoughlin Handout 1.3, page 1 of 6 FUNDAMENTALS OF MATHEMATICS HANDOUT 1.3 DR. MCLOUGHLIN Truth Table for Not K K T F F T Truth Table for And B M B M T F F F T F F F F Truth Table for Or R S R S T
More informationBox. Turn in your e xam to Kathy Stackhouse in Chem 303 by noon on Thursday, March 30.
Phil 201 Exam #6 Score Name Instructions: Open book, open notes. Do all your work on these pages. When doing derivations in this exam, you may use any of the simple, complex, or derived rules of truth-functional
More informationMath Assignment 2 Solutions - Spring Jaimos F Skriletz Provide definitions for the following:
Math 124 - Assignment 2 Solutions - Spring 2009 - Jaimos F Skriletz 1 1. Provide definitions for the following: (a) A statement is a declarative sentence that is either true or false, but not both at the
More informationSection 1.3. Let I be a set. When I is used in the following context,
Section 1.3. Let I be a set. When I is used in the following context, {B i } i I, we call I the index set. The set {B i } i I is the family of sets of the form B i where i I. One could also use set builder
More informationKOÇ UNIVERSITY EQUR 121 FIRST EXAM March 3, 2014
KOÇ UNIVERSITY EQUR 121 FIRST EXAM March 3, 2014 Burak Özbaǧcı Duration of Exam: 75 minutes INSTRUCTIONS: No calculators may be used on the test. No questions, and talking allowed. You must always explain
More informationPre-Algebra Summer Assignment
2018-2019 Pre-Algebra Summer Assignment You must show all work to earn full credit. This assignment will be due Friday, August 24, 2018. It will be worth 50 points. All of these skills are necessary to
More informationAiste: Do you often go to that festival?
Life in Summer Aiste and Christophe discuss summer in their countries. Aiste: Hello, Christophe. So what is summer like in Belgium? Christophe: Well, at first I would like to answer you that summer is
More informationEECS 1028 M: Discrete Mathematics for Engineers
EECS 1028 M: Discrete Mathematics for Engineers Suprakash Datta Office: LAS 3043 Course page: http://www.eecs.yorku.ca/course/1028 Also on Moodle S. Datta (York Univ.) EECS 1028 W 18 1 / 26 Why Study Logic?
More informationLogic and Propositional Calculus
CHAPTER 4 Logic and Propositional Calculus 4.1 INTRODUCTION Many algorithms and proofs use logical expressions such as: IF p THEN q or If p 1 AND p 2, THEN q 1 OR q 2 Therefore it is necessary to know
More informationPredicates, Quantifiers and Nested Quantifiers
Predicates, Quantifiers and Nested Quantifiers Predicates Recall the example of a non-proposition in our first presentation: 2x=1. Let us call this expression P(x). P(x) is not a proposition because x
More informationMath 102 Section 08, Fall 2010 Solutions Practice for Formal Proofs of Arguments
Math 102 Section 08, Fall 2010 Solutions Practice for Formal Proofs of Arguments Basic valid arguments: 1) Law of Detachment, p, q 2) Law of Contraposition, q, p 3) Law of Syllogism, q r, p r 4) Disjunctive
More informationTruth Tables for Arguments
ruth ables for Arguments 1. Comparing Statements: We ve looked at SINGLE propositions and assessed the truth values listed under their main operators to determine whether they were tautologous, self-contradictory,
More informationLOGIC. Name: Teacher: Pd: Page 1
LOGIC Name: Teacher: Pd: Page 1 Table of Contents Day 1 Introduction to Logic HW pages 8-10 Day 2 - Conjunction, Disjunction, Conditionals, and Biconditionals HW pages 16-17 #13-34 all, #35 65(every other
More informationTest 1 Solutions(COT3100) (1) Prove that the following Absorption Law is correct. I.e, prove this is a tautology:
Test 1 Solutions(COT3100) Sitharam (1) Prove that the following Absorption Law is correct. I.e, prove this is a tautology: ( q (p q) (r p)) r Solution. This is Modus Tollens applied twice, with transitivity
More informationPROPOSITIONAL CALCULUS
PROPOSITIONAL CALCULUS A proposition is a complete declarative sentence that is either TRUE (truth value T or 1) or FALSE (truth value F or 0), but not both. These are not propositions! Connectives and
More informationTHE LOGIC OF COMPOUND STATEMENTS
THE LOGIC OF COMPOUND STATEMENTS All dogs have four legs. All tables have four legs. Therefore, all dogs are tables LOGIC Logic is a science of the necessary laws of thought, without which no employment
More informationSection 1.2: Conditional Statements
Section 1.2: Conditional Statements In this section, we study one of the most important tools in logic - conditional statements. Loosely speaking, conditional statements are statements of the form if p
More informationDISCRETE MATHEMATICS BA202
TOPIC 1 BASIC LOGIC This topic deals with propositional logic, logical connectives and truth tables and validity. Predicate logic, universal and existential quantification are discussed 1.1 PROPOSITION
More informationSolutions for the fourth week s homework Math 131
Solutions for the fourth week s homework Math 131 Jason Riedy 15 September, 2008 Also available as PDF. 1 Section 3.1 1.1 Problems 1-5 1. Logical statement: there is enough data to verify the statement.
More informationIntroduction to Sets and Logic (MATH 1190)
Introduction to Sets Logic () Instructor: Email: shenlili@yorku.ca Department of Mathematics Statistics York University Sept 18, 2014 Outline 1 2 Tautologies Definition A tautology is a compound proposition
More informationFill in the blank with either or to make the statement true. A) B)
Edison College MGF 1106 Summer 2008 Practice Midterm Exam Dr. Schnackenberg If you do not agree with the given answers, choose "E" for "None of the above". MULTIPLE CHOICE. Choose the one alternative that
More informationa. ~p : if p is T, then ~p is F, and vice versa
Lecture 10: Propositional Logic II Philosophy 130 3 & 8 November 2016 O Rourke & Gibson I. Administrative A. Group papers back to you on November 3. B. Questions? II. The Meaning of the Conditional III.
More information2. Find all combinations of truth values for p, q and r for which the statement p (q (p r)) is true.
1 Logic Questions 1. Suppose that the statement p q is false. Find all combinations of truth values of r and s for which ( q r) ( p s) is true. 2. Find all combinations of truth values for p, q and r for
More informationPS10.3 Logical implications
Warmup: Construct truth tables for these compound statements: 1) p (q r) p q r p q r p (q r) PS10.3 Logical implications Lets check it out: We will be covering Implications, logical equivalence, converse,
More informationTest Bank Questions. (a) Is there an integer n such that n has? (b) Does there exist such that if n is divided by 4 the remainder is 1 and if?
Discrete Mathematics with Applications, 4th Edition by Susanna S. Epp Chapter 1 Test Bank Questions 1. Fill in the blanks to rewrite the following statement with variables: Is there an integer with a remainder
More informationMACM 101 Discrete Mathematics I. Exercises on Propositional Logic. Due: Tuesday, September 29th (at the beginning of the class)
MACM 101 Discrete Mathematics I Exercises on Propositional Logic. Due: Tuesday, September 29th (at the beginning of the class) SOLUTIONS 1. Construct a truth table for the following compound proposition:
More informationRead ahead and use your textbook to fill in the blanks. We will work the examples together.
Math 1312 Section 1.1 : Sets, Statements, and Reasoning Read ahead and use your textbook to fill in the blanks. We will work the examples together. A set is any. hese objects are called the of the set.
More informationCCHS Math Unit Exam (Ch 1,2,3) Name: Math for Luiberal Arts (200 Points) 9/23/2014
CCHS Math Unit Exam (Ch 1,2,3) Name: Math for Luiberal Arts (200 Points) 9/23/2014 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Let U = {q, r,
More informationMathematical Logic Part One
Mathematical Logic Part One Question: How do we formalize the definitions and reasoning we use in our proofs? Where We're Going Propositional Logic (Today) Basic logical connectives. Truth tables. Logical
More information(p == train arrives late) (q == there are taxis) (r == If p and not q, then r. Not r. p. Therefore, q. Propositional Logic
Propositional Logic The aim of logic in computer science is to develop languages to model the situations we encounter as computer science professionals Want to do that in such a way that we can reason
More informationLogic and Truth Tables
Logic and Truth Tables What is a Truth Table? A truth table is a tool that helps you analyze statements or arguments in order to verify whether or not they are logical, or true. There are five basic operations
More information1.3 Propositional Equivalences
1 1.3 Propositional Equivalences The replacement of a statement with another statement with the same truth is an important step often used in Mathematical arguments. Due to this methods that produce propositions
More informationMath 1312 Lesson 1: Sets, Statements, and Reasoning. A set is any collection of objects. These objects are called the elements of the set.
Math 1312 Lesson 1: Sets, Statements, and Reasoning A set is any collection of objects. hese objects are called the elements of the set. A is a subset of B, if A is "contained" inside B, that is, all elements
More informationSection 1.1: Logical Form and Logical Equivalence
Section 1.1: Logical Form and Logical Equivalence An argument is a sequence of statements aimed at demonstrating the truth of an assertion. The assertion at the end of an argument is called the conclusion,
More informationCHAPTER 1 - LOGIC OF COMPOUND STATEMENTS
CHAPTER 1 - LOGIC OF COMPOUND STATEMENTS 1.1 - Logical Form and Logical Equivalence Definition. A statement or proposition is a sentence that is either true or false, but not both. ex. 1 + 2 = 3 IS a statement
More informationImplications, Quantifiers, and Venn Diagrams. Implications Logical Quantifiers Venn Diagrams. Different Ways of Stating Implications
E6 PPENDIX E Introduction to Logic E.2 Implications, Quantifiers, and Venn Diagrams Implications Logical Quantifiers Venn Diagrams Implications statement of the form If p, then q is called an implication
More informationMathematical Logic Part One
Mathematical Logic Part One Question: How do we formalize the defnitions and reasoning we use in our proofs? Where We're Going Propositional Logic (Today) Basic logical connectives. Truth tables. Logical
More informationMidterm Exam Solution
Midterm Exam Solution Name PID Honor Code Pledge: I certify that I am aware of the Honor Code in effect in this course and observed the Honor Code in the completion of this exam. Signature Notes: 1. This
More informationLogic. Def. A Proposition is a statement that is either true or false.
Logic Logic 1 Def. A Proposition is a statement that is either true or false. Examples: Which of the following are propositions? Statement Proposition (yes or no) If yes, then determine if it is true or
More informationPHIL12A Section answers, 16 February 2011
PHIL12A Section answers, 16 February 2011 Julian Jonker 1 How much do you know? 1. Show that the following sentences are equivalent. (a) (Ex 4.16) A B A and A B A B (A B) A A B T T T T T T T T T T T F
More informationChapter 2: The Logic of Compound Statements
Chapter 2: he Logic of Compound Statements irst: Aristotle (Gr. 384-322 BC) Collection of rules for deductive reasoning to be used in every branch of knowledge Next: Gottfried Leibniz (German, 17th century)
More informationPractice Exam 2. You MUST show all your work, and indicate which value is the main operator value.
Practice Exam 2 You MUS show all your work, and indicate which value is the main operator value. I. ranslate the following statements into symbolic form, using A, B, C, and D. hen, using your knowledge
More informationMathematical Logic Part One
Mathematical Logic Part One An Important Question How do we formalize the logic we've been using in our proofs? Where We're Going Propositional Logic (oday) Basic logical connectives. ruth tables. Logical
More informationLogic and Proofs. Jan COT3100: Applications of Discrete Structures Jan 2007
COT3100: Propositional Equivalences 1 Logic and Proofs Jan 2007 COT3100: Propositional Equivalences 2 1 Translating from Natural Languages EXAMPLE. Translate the following sentence into a logical expression:
More information3/29/2017. Logic. Propositions and logical operations. Main concepts: propositions truth values propositional variables logical operations
Logic Propositions and logical operations Main concepts: propositions truth values propositional variables logical operations 1 Propositions and logical operations A proposition is the most basic element
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name Date A Little Dash of Logic Two Methods of Logical Reasoning Vocabulary Define each term in your own words. 1. inductive reasoning 2. deductive reasoning
More informationDiscrete Mathematical Structures. Chapter 1 The Foundation: Logic
Discrete Mathematical Structures Chapter 1 he oundation: Logic 1 Lecture Overview 1.1 Propositional Logic 1.2 Propositional Equivalences 1.3 Quantifiers l l l l l Statement Logical Connectives Conjunction
More informationPropositional Logic Not Enough
Section 1.4 Propositional Logic Not Enough If we have: All men are mortal. Socrates is a man. Does it follow that Socrates is mortal? Can t be represented in propositional logic. Need a language that talks
More informationCS103 Handout 09 Fall 2012 October 19, 2012 Problem Set 4
CS103 Handout 09 Fall 2012 October 19, 2012 Problem Set 4 This fourth problem set explores propositional and first-order logic, along with its applications. Once you've completed it, you should have a
More informationMath Exam Jam Concise. Contents. 1 Algebra Review 2. 2 Functions and Graphs 2. 3 Exponents and Radicals 3. 4 Quadratic Functions and Equations 4
Contents 1 Algebra Review 2 2 Functions and Graphs 2 3 Exponents and Radicals 3 4 Quadratic Functions and Equations 4 5 Exponential and Logarithmic Functions 5 6 Systems of Linear Equations 6 7 Inequalities
More informationa n d n d n i n n d a o n e o t f o b g b f h n a f o r b c d e f g c a n h i j b i g y i t n d p n a p p s t e v i s w o m e b
Pre-Primer Word Search a n d n d n i n n d a o n e o t f o b g b f h n a f o r b c d e f g c a n h i j b i g y i t n d p n a p p s t e v i s w o m e b and big can for in is it me one 1 Pre-Primer Word
More informationMathematical Logic Part One
Mathematical Logic Part One Question: How do we formalize the definitions and reasoning we use in our proofs? Where We're Going Propositional Logic (oday) Basic logical connectives. ruth tables. Logical
More informationUnit 6 Logic Math 116
Unit 6 Logic Math 116 Logic Unit Statement: A group words or symbols that can be classified as true or false. Examples of statements Violets are blue Five is a natural number I like Algebra 3 + 7 = 10
More informationMath161 HW#2, DUE DATE:
Math161 HW#2, DUE DATE: 07.01.10 Question1) How many students in a class must there be to ensure that 6 students get the same grade (one of A, B, C, D, or F)? Question2) 6 computers on a network are connected
More informationNumbers that are divisible by 2 are even. The above statement could also be written in other logically equivalent ways, such as:
3.4 THE CONDITIONAL & BICONDITIONAL Definition. Any statement that can be put in the form If p, then q, where p and q are basic statements, is called a conditional statement and is written symbolically
More informationPropositional Logic. Argument Forms. Ioan Despi. University of New England. July 19, 2013
Propositional Logic Argument Forms Ioan Despi despi@turing.une.edu.au University of New England July 19, 2013 Outline Ioan Despi Discrete Mathematics 2 of 1 Order of Precedence Ioan Despi Discrete Mathematics
More informationComputer Science 280 Spring 2002 Homework 2 Solutions by Omar Nayeem
Computer Science 280 Spring 2002 Homework 2 Solutions by Omar Nayeem Part A 1. (a) Some dog does not have his day. (b) Some action has no equal and opposite reaction. (c) Some golfer will never be eated
More informationTHE LOGIC OF COMPOUND STATEMENTS
CHAPTER 2 THE LOGIC OF COMPOUND STATEMENTS Copyright Cengage Learning. All rights reserved. SECTION 2.2 Conditional Statements Copyright Cengage Learning. All rights reserved. Conditional Statements Let
More informationFOUNDATION OF COMPUTER SCIENCE ETCS-203
ETCS-203 TUTORIAL FILE Computer Science and Engineering Maharaja Agrasen Institute of Technology, PSP Area, Sector 22, Rohini, Delhi 110085 1 Fundamental of Computer Science (FCS) is the study of mathematical
More informationA spinner has a pointer which can land on one of three regions labelled 1, 2, and 3 respectively.
Math For Liberal Arts Spring 2011 Final Exam. Practice Version Name A spinner has a pointer which can land on one of three regions labelled 1, 2, and 3 respectively. 1) Compute the expected value for the
More informationChapter 1, Section 1.1 Propositional Logic
Discrete Structures Chapter 1, Section 1.1 Propositional Logic These class notes are based on material from our textbook, Discrete Mathematics and Its Applications, 6 th ed., by Kenneth H. Rosen, published
More informationCompound Propositions
Discrete Structures Compound Propositions Producing new propositions from existing propositions. Logical Operators or Connectives 1. Not 2. And 3. Or 4. Exclusive or 5. Implication 6. Biconditional Truth
More informationMath.3336: Discrete Mathematics. Propositional Equivalences
Math.3336: Discrete Mathematics Propositional Equivalences Instructor: Dr. Blerina Xhabli Department of Mathematics, University of Houston https://www.math.uh.edu/ blerina Email: blerina@math.uh.edu Fall
More information2/2/2018. CS 103 Discrete Structures. Chapter 1. Propositional Logic. Chapter 1.1. Propositional Logic
CS 103 Discrete Structures Chapter 1 Propositional Logic Chapter 1.1 Propositional Logic 1 1.1 Propositional Logic Definition: A proposition :is a declarative sentence (that is, a sentence that declares
More informationManual of Logical Style
Manual of Logical Style Dr. Holmes January 9, 2015 Contents 1 Introduction 2 2 Conjunction 3 2.1 Proving a conjunction...................... 3 2.2 Using a conjunction........................ 3 3 Implication
More informationSolutions to Exercises (Sections )
s to Exercises (Sections 1.1-1.10) Section 1.1 Exercise 1.1.1: Identifying propositions (a) Have a nice day. : Command, not a proposition. (b) The soup is cold. : Proposition. Negation: The soup is not
More informationAMTH140 Lecture 8. Symbolic Logic
AMTH140 Lecture 8 Slide 1 Symbolic Logic March 10, 2006 Reading: Lecture Notes 6.2, 6.3; Epp 1.1, 1.2 Logical Connectives Let p and q denote propositions, then: 1. p q is conjunction of p and q, meaning
More informationBoolean Logic Boolean logic combines multiple statements that are either true or false into an expression that is either true or false.
Logic 407 Logic Logic is, basically, the study of valid reasoning. When searching the internet, we use Boolean logic terms like and and or to help us find specific web pages that fit in the sets we are
More informationWORKSHEET. Área: ingles Periodo: 1 Fecha: 26 feb al 2 Mar. Competencia: writing and grammar comprehension. Uses of the past tenses Part I
WORKSHEET Área: ingles Periodo: 1 Fecha: 26 feb al 2 Mar. Tema: Past Tenses Grado: 11th grade Competencia: writing and grammar comprehension Uses of the past tenses Part I The simple past tense is also
More informationFamily Feud Review. Math 1001: Quantitative Skills and Reasoning. September 8, 2011
Review Math 1001: Quantitative Skills and Reasoning September 8, 2011 Question 1 State the definition of an argument. Answer 1 Answer An argument uses a set of facts to support a conclusion. Question 2
More informationDEDUCTIVE REASONING Propositional Logic
7 DEDUCTIVE REASONING Propositional Logic Chapter Objectives Connectives and Truth Values You will be able to understand the purpose and uses of propositional logic. understand the meaning, symbols, and
More informationPropositional Equivalence
Propositional Equivalence Tautologies and contradictions A compound proposition that is always true, regardless of the truth values of the individual propositions involved, is called a tautology. Example:
More information