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)

COMP 170 L2

L07: Intro to Logic

Objective Introduce basic ingredients of the language of logic.

COMP 170 L2

Outline

Example: Logic in programs

Logic statements, truth table, and equivalence

Basic laws about logic statements

Conditional connectives

COMP 170 L2

Logic in Programs

COMP 170 L2

COMP 170 L2

Outline





COMP 170 L2

What make up logic statements?

Symbolic compound statements consist of

Variables, logical connectives, and conditional connectives

COMP 170 L2

Logic Statements

COMP 170 L2

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:

COMP 170 L2

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

COMP 170 L2

Truth Table for Statements Involving ONE Connective

COMP 170 L2

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

COMP 170 L2

Equivalence

COMP 170 L2

COMP 170 L2

Outline





COMP 170 L2

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

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COMP 170 L2

Outline





COMP 170 L2

Conditional Connectives

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COMP 170 L2

Truth Table for Implication

COMP 170 L2

COMP 170 L2

Truth Table for If-and-Only-If

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

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