MAT 142Lecture Video

Series

Truth Tables

Objectives

• Construct a truth table for a given symbolic expression.

• Determine if two given statements are equivalent using truth tables.

• Use De Morgan’s Laws to write a statement equivalent to a given statement.

Vocabulary

• truth table • equivalent expressions • De Morgan’s Laws

Negation

p ~p

T

F

F

T

Conjunctionp q

T T

T F

F T

F F

qp

T

F

F

F

Disjunctionp q

T T

T F

F T

F F

qp

T

T

T

F

Conditionalp q

T T

T F

F T

F F

qp

T

F

T

T

Construct a truth table for:

p ~p

T

F

pp ~

pp ~

T

F T

T

Construct a truth table for: qqp ~

p q

T T

T F

F T

F F

qqp ~ qp q~

Construct a truth table for the following statement:

If the lyrics are not controversial, then the performance is not banned.

p:

q:

The lyrics are controversial.

The performance is banned

Construct a truth table for the following statement:The country singer is in trouble if he is

elected.

p:

q:

The country singer is elected.

The country singer is in trouble.

If he is elected, then the country singer is in trouble.

Construct a truth table for the following statement:If he does not go to jail, he is innocent

or has an alibi.

p:

q:

He goes to jail.

He is innocent.

r: He has an alibi.

Construct a truth tables for: qp ~ qp ~~ and

Construct truth tables to determine whether the following statements are equivalent.

1. The streets are wet or it is not raining.

2. If it is raining, then the streets are wet.

DeMorgan’s Laws

qpqp ~~~

qpqp ~~~

General Negations

pp ~~

qpqp ~~~

qpqp ~~

qpqp ~~~

Creator and Producer

Elizabeth Jones

for

The School of Mathematical and Statistical Sciences

atArizona State University

Videographer

Mike Jones

©2009 Elizabeth Jones and School of Mathematical and Statistical Sciences at Arizona State University