COMP 170 L2 Part 3 of Course Chapter 3 of Textbook.

Slides:



Advertisements
Similar presentations
Logic ChAPTER 3.
Advertisements

TRUTH TABLES Section 1.3.
PROOF BY CONTRADICTION
1 Intro to Logic Supplementary Notes Prepared by Raymond Wong Presented by Raymond Wong.
Propositional Logic. Negation Given a proposition p, negation of p is the ‘not’ of p.
1 Math 306 Foundations of Mathematics I Math 306 Foundations of Mathematics I Goals of this class Introduction to important mathematical concepts Development.
Discrete Mathematics Math 6A Instructor: M. Welling.
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley. All rights reserved.
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley. All rights reserved.
Predicates and Quantifiers
3.2 – Truth Tables and Equivalent Statements
Course Outline Book: Discrete Mathematics by K. P. Bogart Topics:
Chapter 1 The Logic of Compound Statements. Section 1.1 Logical Form and Logical Equivalence.
Chapter 2 Reasoning and Proof. AIM: Introduction to Logic What types of statements are considered mathematical ? Statements in which truth value (either.
BY: MISS FARAH ADIBAH ADNAN IMK. CHAPTER OUTLINE: PART III 1.3 ELEMENTARY LOGIC INTRODUCTION PROPOSITION COMPOUND STATEMENTS LOGICAL.
1 Introduction to Abstract Mathematics The Logic and Language of Proofs Instructor: Hayk Melikya Proposition: Informal introduction to.
Chapter 1, Part II: Predicate Logic With Question/Answer Animations.
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley. All rights reserved.
Logic Disjunction A disjunction is a compound statement formed by combining two simple sentences using the word “OR”. A disjunction is true when at.
Barnett/Ziegler/Byleen Finite Mathematics 11e1 Chapter 7 Review Important Terms, Symbols, Concepts 7.1. Logic A proposition is a statement (not a question.
Chapter 2: The Logic of Compound Statements 2.2 Conditional Statements
Lecture Propositional Equivalences. Compound Propositions Compound propositions are made by combining existing propositions using logical operators.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 3 Logic.
Chapter 3: Introduction to Logic. Logic Main goal: use logic to analyze arguments (claims) to see if they are valid or invalid. This is useful for math.
Chapter 8 – Symbolic Logic Professor D’Ascoli. Symbolic Logic Because the appraisal of arguments is made difficult by the peculiarities of natural language,
How do I show that two compound propositions are logically equivalent?
Thinking Mathematically
Chapter 1: The Foundations: Logic and Proofs
COMP 170 L2 L08: Quantifiers. COMP 170 L2 Outline l Quantifiers: Motivation and Concepts l Quantifiers: Notations and Meaning l Saying things with Quantified.
Chapter 2 Symbolic Logic. Section 2-1 Truth, Equivalence and Implication.
TRUTH TABLES. Introduction The truth value of a statement is the classification as true or false which denoted by T or F. A truth table is a listing of.
 2012 Pearson Education, Inc. Slide Chapter 3 Introduction to Logic.
Mathematics for Computing Lecture 2: Computer Logic and Truth Tables Dr Andrew Purkiss-Trew Cancer Research UK
 2012 Pearson Education, Inc. Slide Chapter 3 Introduction to Logic.
Thinking Mathematically Logic 3.4 Truth Tables for the Conditional and Biconditional.
3.3 – The Conditional A conditional statement is a compound statement that uses the connective if…then. The conditional is written with an arrow, so “if.
 Statement - sentence that can be proven true or false  Truth value – true or false  Statements are often represented using letters such as p and q.
COMP 170 L2 Page 1 Review for Midterm 2 Part II: Number Theory and Cryptography L06: RSA Part III: Logic L07, L08, L09 Part IV: Induction and Recurrence.
CS-7081 Application - 1. CS-7082 Example - 2 CS-7083 Simplifying a Statement – 3.
Chapter 1 – Part 3 ELEMENTARY LOGIC
Chapter 1 Propositional Logic
Introduction to Logic © 2008 Pearson Addison-Wesley.
Presented by: Tutorial Services The Math Center
AND.
DISCRETE MATHEMATICS CHAPTER I.
Truth Tables and Equivalent Statements
CHAPTER 2 Boolean Algebra
Classwork/Homework Classwork – Page 90 (11 – 49 odd)
How do I show that two compound propositions are logically equivalent?
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
Chapter 8 Logic Topics
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
2 Chapter Introduction to Logic and Sets
Information Technology Department
Chapter 1 The Foundations: Logic and Proof, Sets, and Functions
Chapter 3 Introduction to Logic © 2008 Pearson Addison-Wesley.
TRUTH TABLES.
Chapter 1 Logic and Proof.
(1.4) An Introduction to Logic
Discrete Mathematics and Its Applications Kenneth H
Chapter 3 Introduction to Logic 2012 Pearson Education, Inc.
Logical Truth To show a statement A is a logic truth (tautology) ...
Lecture 5 Binary Operation Boolean Logic. Binary Operations Addition Subtraction Multiplication Division.
Truth tables Mrs. Palmer.
1.2 Propositional Equivalences
Section 3.3 Truth Tables for the Conditional and Biconditional
1.3 Propositional Equivalences
CHAPTER 3 Logic.
Truth Tables for Conditional and Biconditional Statements
boolean Expressions Relational, Equality, and Logical Operators
Presentation transcript:

COMP 170 L2 Part 3 of Course Chapter 3 of Textbook

COMP 170 L2 Introduction to Part 3 l Objectives  Introduce the basics of logic (L07, L08)  Develop a language for talking about proofs  Discuss the logic principles behind proofs (L09) Page 2

COMP 170 L2 L07: Intro to Logic l Objective n Introduce basic ingredients of the language of logic. Page 3

COMP 170 L2 Outline l Example: Logic in programs l Logic statements, truth table, and equivalence l Basic laws about logic statements l Conditional connectives Page 4

COMP 170 L2 Logic in Programs Page 5

COMP 170 L2 Logic in Programs Page 6

COMP 170 L2 Page 7

COMP 170 L2 Outline l Example: Logic in programs l Logic statements, truth table, and equivalence l Basic laws about logic statements l Conditional connectives Page 8

COMP 170 L2 What make up logic statements? l Symbolic compound statements consist of n Variables, logical connectives, and conditional connectives Page 9

COMP 170 L2 Logic Statements Page 10

COMP 170 L2 Logic Statements can be True or False l Variables such as s, t, u can be either true (T) or false (F) l Meaning of connectives as follows: Page 11

COMP 170 L2 Truth Table for Logic Statements l Variables such as s, t, u can be either true (T) or false (F) n Many possible scenarios  s = T, t=T, u=T;  s = T, t=T, u=F;  s = T, t=F, u=T;  …. l Truth table n Shows whether a compound statement is true for false in all cases n Allow us to determine whether two statements are equivalent Page 12

COMP 170 L2 Truth Table for Statements Involving ONE Connective Page 13

COMP 170 L2 l The two programs are equivalent because they are true in the same scenarios. Page 14

COMP 170 L2 Equivalence Page 15

COMP 170 L2 Page 16

COMP 170 L2 Outline l Example: Logic in programs l Logic statements, truth table, and equivalence l Basic laws about logic statements l Conditional connectives Page 17

COMP 170 L2 Page 18 Also: w \/ ( u /\ v) = (w \/ u ) /\ (w /\ v)

COMP 170 L2 Page 19

COMP 170 L2 Page 20

COMP 170 L2 Outline l Example: Logic in programs l Logic statements, truth table, and equivalence l Basic laws about logic statements l Conditional connectives Page 21

COMP 170 L2 Conditional Connectives Page 22

COMP 170 L2 Page 23

COMP 170 L2 Page 24

COMP 170 L2 Page 25 Truth Table for Implication

COMP 170 L2 Page 26 Truth Table for Implication

COMP 170 L2 Truth Table for Implication Page 27

COMP 170 L2 Page 28

COMP 170 L2 Page 29 Truth Table for If-and-Only-If

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.