COMP 170 L2 Part 3 of Course Chapter 3 of Textbook

COMP 170 L2

Part 3 of Course

Chapter 3 of Textbook

COMP 170 L2

Introduction to Part 3

Objectives Introduce the basics of logic (L07, L08)

Develop a language for talking about proofs

Discuss the logic principles behind proofs (L09)

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L07: Intro to Logic

Objective Introduce basic ingredients of the language of logic.

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Outline

Example: Logic in programs

Logic statements, truth table, and equivalence

Basic laws about logic statements

Conditional connectives

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Logic in ProgramsPage 5

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Logic in ProgramsPage 6

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COMP 170 L2

Outline

Example: Logic in programs

Logic statements, truth table, and equivalence

Basic laws about logic statements

Conditional connectives

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What make up logic statements?

Symbolic compound statements consist of

Variables, logical connectives, and conditional connectives

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Logic StatementsPage 10

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Logic Statements can be True or False

Variables such as s, t, u can be either true (T) or false (F)

Meaning of connectives as follows:

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Truth Table for Logic Statements

Variables such as s, t, u can be either true (T) or false (F) Many possible scenarios

s = T, t=T, u=T;

s = T, t=T, u=F;

s = T, t=F, u=T;

….

Truth table Shows whether a compound statement is true for false in all cases Allow us to determine whether two statements are equivalent

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Truth Table for Statements Involving ONE Connective

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The two programs are equivalent because they are true in the same scenarios.

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EquivalencePage 15

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Outline

Example: Logic in programs

Logic statements, truth table, and equivalence

Basic laws about logic statements

Conditional connectives

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Also: w \/ ( u /\ v) = (w \/ u ) /\ (w /\ v)

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COMP 170 L2

Outline

Example: Logic in programs

Logic statements, truth table, and equivalence

Basic laws about logic statements

Conditional connectives

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Conditional ConnectivesPage 22

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Truth Table for Implication

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Truth Table for Implication

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Truth Table for ImplicationPage 27

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Truth Table for If-and-Only-If