Truth Tables

1
Truth Tables
2
Objectives

• Construct a truth table for a given symbolic
  expression.
• Determine if two given statements are equivalent
  using truth tables.
• Use De Morgans Laws to write a statement
  equivalent to a given statement.

3
Vocabulary

• truth table
• equivalent expressions
• De Morgans Laws

4
Negation
p p
T
F
F
T
5
Conjunction
p q
T T
T F
F T
F F
T
F
F
F
6
Disjunction
p q
T T
T F
F T
F F
T
T
T
F
7
Conditional
p q
T T
T F
F T
F F
T
F
T
T
8
Construct a truth table for
p p
T
F
F
T
T
T
9
Construct a truth table for
p q
T T
T F
F T
F F
10
Construct a truth table for the following
statement

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

p
The lyrics are controversial.
q
The performance is banned
11
Construct a truth table for the following
statement

• The country singer is in trouble if he is elected.

If he is elected, then the country singer is in
trouble.
p
The country singer is elected.
q
The country singer is in trouble.
12
Construct a truth table for the following
statement

• If he does not go to jail, he is innocent or has
  an alibi.

p
He goes to jail.
q
He is innocent.
r
He has an alibi.
13
Construct a truth tables for
and
14
Construct truth tables to determine whether the
following statements are equivalent.

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

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

15
DeMorgans Laws
16
General Negations