CSCI Homework Set 1 Due: September 11, 2018 at the beginning of class
|
|
|
- Hilary Hawkins
- 5 years ago
- Views:
Transcription
1 CSCI 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 make sure they are secured together. Problem 1 Indicate whether each statement below is a proposition. If the statement is a proposition, express the negation of the proposition in English or mathematical symbols. a. 0 < x < 10. No b. π is approximately 22/7. Yes; π is not approximately 22/7 c. Pay attention in class. No d. All years divisible by 4 are leap years. Yes; Not all years divisible by 4 are leap years. Problem 2 he propositional variables, p, q, and s have the following truth assignments: p =, q = F, r = F. Give the truth value for the following compound propositions: a. p q b. q r F c. p r F d. r Problem 3 he values for the propositional variables p, q, r, s, are determined as follows: p = q = F r = F s = Determine the truth values for the following propositions: a. (p q) s b. (r q) p c. (s q) (p q)
2 d. (r p) s e. p (q s) Problem 4 Give a truth table for the following propositions: a. (p q) (q p) p q p q q p (p q) (q p) F F F F F F F F b. p ( p q) p q p p q p ( p q) F F F F F F F F F F c. (p r) (r q) p q r r p r (r q) (p r) (r q) F F F F F F F F F F F F F F F F F F F F F F F F F Problem 5 Let p and q be the propositions p : I bought a lottery ticket this week. q : I won the million dollar jackpot. Express each of these propositions as an English sentence. a. p q I bought a lottery ticket this week or I didn t win the million dollar jackpot b. p q If I bought a lottery ticket this week, then I won the million dollar jackpot
3 c. p q I bought a lottery ticket this week if and only if I won the million dollar jackpot d. p q If I didn t buy a lottery ticket this week then I will not win the million dollar jackpot e. p q I didn t buy a lottery ticket this week and I didn t win the million dollar jackpot f. p (p q) I didn t buy a lottery ticket this week or I bought a lottery ticket this week and won the million dollar jackpot. Problem 6 Let p, q, and r be the propositions p : You get an A on the final exam. q : You do every exercise in this book. r : You get an A in this class. Write these propositions using p, q, and r and logical connectives (including negations). a. You get an A in this class, but you do not do every exercise in this book. r q b. You get an A on the final, you do every exercise in this book, and you get an A in this class. p q r c. o get an A in this class, it is necessary for you to get an A on the final. p r d. You get an A on the final, but you don t do every exercise in this book; nevertheless, you get an A in this class. p q r e. Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class. (p q) r Problem 7 Find out for each of the following propositions whether it is a tautology, a contradiction, or neither (a contingency). Prove your answer (use a truth table).
4 a. [(p q) (q r)] (p r) p q r p q q r (p q) (q r) p r [(p q) (q r)] (p r) F F F F F F F F F F F F F F F F F F F F F F So it is a tautology. b. (p q r) [(q r) (p q)] p q r p q r p q q r (q r) (p q) (p q r) [(q r) (p q)] F F F F F F F F F F F F F F F F F F F F F F F F F So it is a contingency. Problem 8 For each table, give a logical expression whose truth table is the same as the one given below (note that there may be several correct answers): a. p q? F F F F F F F his could be p q or ( p q) or
5 b. p q? F F F F F his could be p q or ( p q) or Problem 9 Consider the following sentence: here is a student in this class who has taken some course in every department in the College of Engineering and Computer Science. a. Express the sentence using quantifiers (and logical propositions). You should use the variables: s student, c course, d department, and these should be the only variables. Give the domain of each variable. b. Find the logical negation of the quantifier expression that you obtained in (a). c. ranslate the negation you obtained in (b) into an English sentence. a. Define the following variables and domains Variable Domain s student this class c course all courses d department departments in the College We define the propositional function: P(s, c, d) = s took course c in department d. hen the sentence can be written as s d c P(s, c, d). b. he negation is s d c P(s, c, d). c. In English: Every student in this class has not taken any course in some department in the College.
CS100: 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
Overview. 1. Introduction to Propositional Logic. 2. Operations on Propositions. 3. Truth Tables. 4. Translating Sentences into Logical Expressions
Note 01 Propositional Logic 1 / 10-1 Overview 1. Introduction to Propositional Logic 2. Operations on Propositions 3. Truth Tables 4. Translating Sentences into Logical Expressions 5. Preview: Propositional
Discrete 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
Introduction 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
LOGIC 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,
Math.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
CS1021. Why logic? Logic about inference or argument. Start from assumptions or axioms. Make deductions according to rules of reasoning.
3: Logic Why logic? Logic about inference or argument Start from assumptions or axioms Make deductions according to rules of reasoning Logic 3-1 Why logic? (continued) If I don t buy a lottery ticket on
Example. Logic. Logical Statements. Outline of logic topics. Logical Connectives. Logical Connectives
Logic Logic is study of abstract reasoning, specifically, concerned with whether reasoning is correct. Logic focuses on relationship among statements as opposed to the content of any particular statement.
CSC 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,...)
Practice 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
PROPOSITIONAL 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
Section L.1- Introduction to Logic
Section L.1- Introduction to Logic Definition: A statement, or proposition, is a declarative sentence that can be classified as either true or false, but not both. Example 1: Which of the following are
Total score: /100 points
Points missed: Student's Name: Total score: /100 points East Tennessee State University Department of Computer and Information Sciences CSCI 710 (Tarnoff) Discrete Structures TEST for Spring Semester,
Homework assignment 1: Solutions
Math 240: Discrete Structures I Due 4:30pm Friday 29 September 2017. McGill University, Fall 2017 Hand in to the mailbox at Burnside 1005. Homework assignment 1: Solutions Discussing the assignment with
Supplementary exercises in propositional logic
Supplementary exercises in propositional logic The purpose of these exercises is to train your ability to manipulate and analyze logical formulas. Familiarize yourself with chapter 7.3-7.5 in the course
Sec 3.3 The Conditional & Circuits
Sec 3.3 The Conditional & Circuits Conditional statement: connective if... then. a compound statement that uses the Conditional statements are also known as implications, and can be written as: p q (pronounced
Math 13, Spring 2013, Lecture B: Midterm
Math 13, Spring 2013, Lecture B: Midterm Name Signature UCI ID # E-mail address Each numbered problem is worth 12 points, for a total of 84 points. Present your work, especially proofs, as clearly as possible.
Logic 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:
Section 3.1. Statements and Logical Connectives. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 3.1 Statements and Logical Connectives What You Will Learn Statements, quantifiers, and compound statements Statements involving the words not, and, or, if then, and if and only if 3.1-2 HISORY
1.3 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
A statement is a sentence that is definitely either true or false but not both.
5 Logic In this part of the course we consider logic. Logic is used in many places in computer science including digital circuit design, relational databases, automata theory and computability, and artificial
Discrete Mathematics. Sec
Islamic University of Gaza Faculty of Engineering Department of Computer Engineering Fall 2011 ECOM 2311: Discrete Mathematics Eng. Ahmed Abumarasa Discrete Mathematics Sec 1.1-1.6 The Foundations: Logic
n logical not (negation) n logical or (disjunction) n logical and (conjunction) n logical exclusive or n logical implication (conditional)
Discrete Math Review Discrete Math Review (Rosen, Chapter 1.1 1.6) TOPICS Propositional Logic Logical Operators Truth Tables Implication Logical Equivalence Inference Rules What you should know about propositional
Chapter 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
Proposition/Statement. Boolean Logic. Boolean variables. Logical operators: And. Logical operators: Not 9/3/13. Introduction to Logical Operators
Proposition/Statement Boolean Logic CS 231 Dianna Xu A proposition is either true or false but not both he sky is blue Lisa is a Math major x == y Not propositions: Are you Bob? x := 7 1 2 Boolean variables
Compound 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
ECOM Discrete Mathematics
ECOM 2311- Discrete Mathematics Chapter # 1 : The Foundations: Logic and Proofs Fall, 2013/2014 ECOM 2311- Discrete Mathematics - Ch.1 Dr. Musbah Shaat 1 / 85 Outline 1 Propositional Logic 2 Propositional
Examples. Example (1) Example (2) Let x, y be two variables, and denote statements p : x = 0 and q : y = 1. Solve. x 2 + (y 1) 2 = 0.
Examples Let x, y be two variables, and denote statements p : x = 0 and q : y = 1. Example (1) Solve x 2 + (y 1) 2 = 0. The solution is x = 0 AND y = 1. [p q.] Example (2) Solve x(y 1) = 0. Examples Let
Announcements. CS311H: Discrete Mathematics. Propositional Logic II. Inverse of an Implication. Converse of a Implication
Announcements CS311H: Discrete Mathematics Propositional Logic II Instructor: Işıl Dillig First homework assignment out today! Due in one week, i.e., before lecture next Wed 09/13 Remember: Due before
Truth 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,
Lecture 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
Logic Overview, I. and T T T T F F F T F F F F
Logic Overview, I DEFINITIONS A statement (proposition) is a declarative sentence that can be assigned a truth value T or F, but not both. Statements are denoted by letters p, q, r, s,... The 5 basic logical
1.1 Language and Logic
c Oksana Shatalov, Fall 2017 1 1.1 Language and Logic Mathematical Statements DEFINITION 1. A proposition is any declarative sentence (i.e. it has both a subject and a verb) that is either true or false,
Section 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,
CHAPTER 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
Section 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
Mat 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
HOMEWORK 1: SOLUTIONS - MATH 215 INSTRUCTOR: George Voutsadakis
HOMEWORK 1: SOLUTIONS - MATH 215 INSTRUCTOR: George Voutsadakis Problem 1 Make truth tables for the propositional forms (P Q) (P R) and (P Q) (R S). Solution: P Q R P Q P R (P Q) (P R) F F F F F F F F
1.1 Language and Logic
c Oksana Shatalov, Spring 2018 1 1.1 Language and Logic Mathematical Statements DEFINITION 1. A proposition is any declarative sentence (i.e. it has both a subject and a verb) that is either true or false,
Solutions to Homework I (1.1)
Solutions to Homework I (1.1) Problem 1 Determine whether each of these compound propositions is satisable. a) (p q) ( p q) ( p q) b) (p q) (p q) ( p q) ( p q) c) (p q) ( p q) (a) p q p q p q p q p q (p
Propositional 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:
Test 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
EECS 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?
Section A (not in the text) Which of the following are statements? Explain. 3. The President of the United States in 2089 will be a woman.
Math 299 Homework Assignment, Chapter 2 Section 2.1 2.A (not in the text) Which of the following are statements? Explain. 1. Let x be a positive integer. Then x is rational. 2. Mathematics is fun. 3. The
Announcements. CS243: Discrete Structures. Propositional Logic II. Review. Operator Precedence. Operator Precedence, cont. Operator Precedence Example
Announcements CS243: Discrete Structures Propositional Logic II Işıl Dillig First homework assignment out today! Due in one week, i.e., before lecture next Tuesday 09/11 Weilin s Tuesday office hours are
Solving and Graphing Inequalities Joined by And or Or
Solving and Graphing Inequalities Joined by And or Or Classwork 1. Zara solved the inequality 18 < 3x 9 as shown below. Was she correct? 18 < 3x 9 27 < 3x 9 < x or x> 9 2. Consider the compound inequality
Logical Operators. Conjunction Disjunction Negation Exclusive Or Implication Biconditional
Logical Operators Conjunction Disjunction Negation Exclusive Or Implication Biconditional 1 Statement meaning p q p implies q if p, then q if p, q when p, q whenever p, q q if p q when p q whenever p p
THE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DISCRETE MATHMATICS DISCUSSION ECOM Eng. Huda M.
THE ISLAMIC UNIVERSITY OF GAZA ENGINEERING FACULTY DEPARTMENT OF COMPUTER ENGINEERING DISCRETE MATHMATICS DISCUSSION ECOM 2011 Eng. Huda M. Dawoud September, 2015 Section 1: Propositional Logic 2. Which
DISCRETE STRUCTURES WEEK5 LECTURE1
DISCRETE STRUCTURES WEEK5 LECTURE1 Let s get started with... Logic! Spring 2010 CPCS 222 - Discrete Structures 2 Logic Crucial for mathematical reasoning Important for program design Used for designing
Intro to Logic and Proofs
Intro to Logic and Proofs Propositions A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both. Examples: It is raining today. Washington
PS10.3 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,
Introduction to Decision Sciences Lecture 2
Introduction to Decision Sciences Lecture 2 Andrew Nobel August 24, 2017 Compound Proposition A compound proposition is a combination of propositions using the basic operations. For example (p q) ( p)
Functions. Lecture 4: Truth functions, evaluating compound statements. Arithmetic Functions. x y x+y
Lecture 4: ruth functions, evaluating compound statements 1. unctions, arithmetic functions, and truth functions 2. Definitions of truth functions unctions A function is something that takes inputs and
CSE 20: Discrete Mathematics
Spring 2018 Summary Last time: Today: Logical connectives: not, and, or, implies Using Turth Tables to define logical connectives Logical equivalences, tautologies Some applications Proofs in propositional
1 FUNDAMENTALS OF LOGIC NO.10 HERBRAND THEOREM Tatsuya Hagino hagino@sfc.keio.ac.jp lecture URL https://vu5.sfc.keio.ac.jp/slide/ 2 So Far Propositional Logic Logical connectives (,,, ) Truth table Tautology
2. 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
ANS: If you are in Kwangju then you are in South Korea but not in Seoul.
Math 15 - Spring 2017 - Homework 1.1 and 1.2 Solutions 1. (1.1#1) Let the following statements be given. p = There is water in the cylinders. q = The head gasket is blown. r = The car will start. (a) Translate
C241 Homework Assignment 4
C241 Homework Assignment 4 1. Which of the following formulas are tautologies and which are contradictions? Which of the formulas are logically equivalent to each other? (a) p (q r) (b) ( p r) (q r) (c)
Chapter 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
Discrete Mathematics and Applications COT3100
Discrete Mathematics and Applications CO3100 Dr. Ungor Sources: Slides are based on Dr. G. Bebis material. uesday, January 7, 2014 oundations of Logic: Overview Propositional logic: (Sections 1.1-1.3)
Full file at
1 Logic and Proofs 1.1 Propositions and Connectives 1. (a) true (b) false (c) true (d) false (e) false (f) false (g) false (h) false 2. (a) Not a proposition (b) False proposition (c) Not a proposition.
Recall that the expression x > 3 is not a proposition. Why?
Predicates and Quantifiers Predicates and Quantifiers 1 Recall that the expression x > 3 is not a proposition. Why? Notation: We will use the propositional function notation to denote the expression "
Mathematical Reasoning (Part I) 1
c Oksana Shatalov, Spring 2017 1 Mathematical Reasoning (art I) 1 Statements DEFINITION 1. A statement is any declarative sentence 2 that is either true or false, but not both. A statement cannot be neither
CSE 240 Logic and Discrete Mathematics
CSE 240 Logic and Discrete Mathematics Instructor: odd Sproull Department of Computer Science and Engineering Washington University in St. Louis 1Extensible - CSE 240 Logic Networking and Discrete Platform
CS 173: Discrete Mathematical Structures, Spring 2008 Homework 1 Solutions
CS 173: Discrete Mathematical Structures, Spring 2008 Homework 1 Solutions 1. [10 points] Translate the following sentences into propositional logic, making the meaning of your propositional variables
2/13/2012. Logic: Truth Tables. CS160 Rosen Chapter 1. Logic?
Logic: Truth Tables CS160 Rosen Chapter 1 Logic? 1 What is logic? Logic is a truth-preserving system of inference Truth-preserving: If the initial statements are true, the inferred statements will be true
DISCRETE 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
Deductive and Inductive Logic
Deductive Logic Overview (1) Distinguishing Deductive and Inductive Logic (2) Validity and Soundness (3) A Few Practice Deductive Arguments (4) Testing for Invalidity (5) Practice Exercises Deductive and
MACM 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:
CS 2740 Knowledge Representation. Lecture 4. Propositional logic. CS 2740 Knowledge Representation. Administration
Lecture 4 Propositional logic Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square dministration Homework assignment 1 is out Due next week on Wednesday, September 17 Problems: LISP programming a PL
Logical Representations. LING 7800/CSCI 7000 Martha Palmer 9/30/2014
Logical Representations LING 7800/CSCI 7000 Martha Palmer 9/30/2014 1 The Semantic Wall Physical Symbol System World +BLOCKA+ +BLOCKB+ +BLOCKC+ P 1 :(IS_ON +BLOCKA+ +BLOCKB+) P 2 :((IS_RED +BLOCKA+) Truth
Logic as a Tool Chapter 1: Understanding Propositional Logic 1.1 Propositions and logical connectives. Truth tables and tautologies
Logic as a Tool Chapter 1: Understanding Propositional Logic 1.1 Propositions and logical connectives. Truth tables and tautologies Valentin Stockholm University September 2016 Propositions Proposition:
software design & management Gachon University Chulyun Kim
Gachon University Chulyun Kim 2 Outline Propositional Logic Propositional Equivalences Predicates and Quantifiers Nested Quantifiers Rules of Inference Introduction to Proofs 3 1.1 Propositional Logic
1) Let h = John is healthy, w = John is wealthy and s = John is wise Write the following statement is symbolic form
Math 378 Exam 1 Spring 2009 Show all Work Name 1) Let h = John is healthy, w = John is wealthy and s = John is wise Write the following statement is symbolic form a) In order for John to be wealthy it
Write the negation of each of the following propositions without using any form of the word not :
Write the negation of each of the following propositions without using any form of the word not : Today is Thursday Today is Monday or Tuesday or Wednesday or Friday or Saturday or Sunday 2 + 1 = 3 2+1
Course Staff. Textbook
Course Staff CS311H: Discrete Mathematics Intro and Propositional Logic Instructor: Işıl Dillig Instructor: Prof. Işıl Dillig TAs: Jacob Van Geffen, Varun Adiga, Akshay Gupta Class meets every Monday,
Review. Propositional Logic. Propositions atomic and compound. Operators: negation, and, or, xor, implies, biconditional.
Review Propositional Logic Propositions atomic and compound Operators: negation, and, or, xor, implies, biconditional Truth tables A closer look at implies Translating from/ to English Converse, inverse,
Discrete Mathematics Recitation Course 張玟翔
Discrete Mathematics Recitation Course 1 2013.03.07 張玟翔 Acknowledge 鄭安哲 TA 2012 About Myself English Name : Zak Chinese Name : 張玟翔 Mail:o0000032@yahoo.com.tw Lab: ED612 1-1 Propositional Logic 1-1 Ex.2
A = LW V = LWH. P = a + b + c T = CN + F. d = rt P = 2(L +W ) = 2L + 2W 635 = 2N N / N = 510 / N N = 255
Free Pre-Algebra Lesson 18! page 1 Lesson 18 Writing Equations for Word Problems Math on the Street New York City math teacher George Nobl had a table in Times Square where he gave out candy bars to passers-by
Introduction Propositional Logic. Discrete Mathematics Andrei Bulatov
Introduction Propositional Logic Discrete Mathematics Andrei Bulatov Discrete Mathematics Propositional Logic 2-2 What is Logic? Computer science is a mere continuation of logic by other means Georg Gottlob
The Logic of Compound Statements cont.
The Logic of Compound Statements cont. CSE 215, Computer Science 1, Fall 2011 Stony Brook University http://www.cs.stonybrook.edu/~cse215 Refresh from last time: Logical Equivalences Commutativity of :
(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
2/2/2018. 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
PL: Truth Trees. Handout Truth Trees: The Setup
Handout 4 PL: Truth Trees Truth tables provide a mechanical method for determining whether a proposition, set of propositions, or argument has a particular logical property. For example, we can show that
Proving logical equivalencies (1.3)
EECS 203 Spring 2016 Lecture 2 Page 1 of 6 Proving logical equivalencies (1.3) One thing we d like to do is prove that two logical statements are the same, or prove that they aren t. Vocabulary time In
CHAPTER 2 INTRODUCTION TO CLASSICAL PROPOSITIONAL LOGIC
CHAPTER 2 INTRODUCTION TO CLASSICAL PROPOSITIONAL LOGIC 1 Motivation and History The origins of the classical propositional logic, classical propositional calculus, as it was, and still often is called,
PLEASE HAND IN PLEASE HAND IN. Solutions Sample
PLEASE HAND IN UNIVERSITY OF TORONTO Faculty of Arts and Science Term test #1 CSC 165H1 Section L0101 Duration 60 minutes PLEASE HAND IN No aids allowed Last Name: First Name: Solutions Sample Student
Logic. 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
CS1800 Discrete Structures Spring 2018 February CS1800 Discrete Structures Midterm Version A
CS1800 Discrete Structures Spring 2018 February 2018 CS1800 Discrete Structures Midterm Version A Instructions: 1. The exam is closed book and closed notes. You may not use a calculator or any other electronic
Tautologies, Contradictions, and Contingencies
Section 1.3 Tautologies, Contradictions, and Contingencies A tautology is a proposition which is always true. Example: p p A contradiction is a proposition which is always false. Example: p p A contingency
Department of Computer Science & Software Engineering Comp232 Mathematics for Computer Science
Department of Computer Science & Software Engineering Comp232 Mathematics for Computer Science Fall 2018 Assignment 1. Solutions 1. For each of the following statements use a truth table to determine whether
n Empty Set:, or { }, subset of all sets n Cardinality: V = {a, e, i, o, u}, so V = 5 n Subset: A B, all elements in A are in B
Discrete Math Review Discrete Math Review (Rosen, Chapter 1.1 1.7, 5.5) TOPICS Sets and Functions Propositional and Predicate Logic Logical Operators and Truth Tables Logical Equivalences and Inference
Conditional Statements
Conditional Statements Lecture 3 Section 2.2 Robb T. Koether Hampden-Sydney College Fri, Jan 17, 2014 Robb T. Koether (Hampden-Sydney College) Conditional Statements Fri, Jan 17, 2014 1 / 26 1 Conditional
Department of Mathematics and Statistics Math B: Discrete Mathematics and Its Applications Test 1: October 19, 2006
Department of Mathematics and Statistics Math 1019 3.0 B: Discrete Mathematics and Its Applications est 1: October 19, 2006 Name: (Last/amily) (irst) Student No. Instructions: 1. his test has 8 questions
Announcements CompSci 102 Discrete Math for Computer Science
Announcements CompSci 102 Discrete Math for Computer Science Read for next time Chap. 1.4-1.6 Recitation 1 is tomorrow Homework will be posted by Friday January 19, 2012 Today more logic Prof. Rodger Most
It is not the case that ϕ. p = It is not the case that it is snowing = It is not. r = It is not the case that Mary will go to the party =
Introduction to Propositional Logic Propositional Logic (PL) is a logical system that is built around the two values TRUE and FALSE, called the TRUTH VALUES. true = 1; false = 0 1. Syntax of Propositional
Preparing for the CS 173 (A) Fall 2018 Midterm 1
Preparing for the CS 173 (A) Fall 2018 Midterm 1 1 Basic information Midterm 1 is scheduled from 7:15-8:30 PM. We recommend you arrive early so that you can start exactly at 7:15. Exams will be collected
Predicates and Quantifiers
Predicates and Quantifiers Lecture 9 Section 3.1 Robb T. Koether Hampden-Sydney College Wed, Jan 29, 2014 Robb T. Koether (Hampden-Sydney College) Predicates and Quantifiers Wed, Jan 29, 2014 1 / 32 1
ECS 20: Discrete Mathematics for Computer Science UC Davis Phillip Rogaway June 12, Final Exam
ECS 20: Discrete Mathematics for Computer Science Handout F UC Davis Phillip Rogaway June 12, 2000 Final Exam Instructions: Read the questions carefully; maybe I m not asking what you assume me to be asking!
Learning Goals of CS245 Logic and Computation
Learning Goals of CS245 Logic and Computation Alice Gao April 27, 2018 Contents 1 Propositional Logic 2 2 Predicate Logic 4 3 Program Verification 6 4 Undecidability 7 1 1 Propositional Logic Introduction