# GNED 1101 Chapter Notes - Chapter 1.4-1.5: Logical Biconditional, Truth Table, Contraposition

1.4 Truth Tables for Conditional and Biconditional

Conditional Truth Table (If/Then)

P

Q

P Q

T

T

T

T

F

F

F

T

T

F

F

T

***A conditional is false only when the antecedent is true and the consequent is false

Example 1

o q p

P Q

Q

p

q p

T T

F

F

T

T F

T

F

F

F T

F

T

T

F F

T

T

T

Notice that pq, and q p have the same truth value in each of the four cases

o So whenever there is a conditional statement, you can reverse and negate the antecedent and

consequent, and the statement’s truth value will not change

o Ie; these two statements have the same truth value

If you’re cool, you wont wear clothing with your school name on it

If you wear clothing with your school name on it, youre not cool

Example 2 [(p q) p] q

P Q

P q

(false only when

both are false)

p

(pq) p

(

is true only

when p

q and

p

are true)

[(pq) p] q

(

is false only

when (p

q)

p)

is true and q is

false)

T T

T

F

F

T

T F

T

F

F

T

F T

T

T

T

T

F F

F

T

F

T

** a tautology is a compound statement that is always true, [(pq) p] q is a tautology

**conditional statements that are tautologies are called implications

Biconditional if and only if

The Biconditional statement pq means that pq and qp. This is written as

o (pq) (qp)

P Q

PQ

QP

(PQ) (QP)

T T

T

T

T

T F

F

T

F

F T

T

T

F

F F

T

T

T

A biconditional is true only when the component statements have the same truth value (both true or both

false)

## Document Summary

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