# Truth tables

### Truth tables

#### Lessons

Notes:

We can organize truth values of statements by using a truth table.
• Introduction
Truth Tables Overview:
a)
Negation Truth Tables

b)
Conjunction Truth Tables

c)
Disjunction Truth Tables

d)
Truth Tables with three or more statements

• 1.
Truth Tables with Negations, Conjunctions, and Disjunctions (two statements)

Fill in the truth tables:

a)
 $p$ $q$ ~$p$ ~$p$ ˅ $q$ T T T F F T F F

b)
 $p$ $q$ ~$q$ $p$ ˄ ~$q$ T T T F F T F F

c)
 $p$ $q$ ~$p$ ~$q$ ~$p$ ˄ ~$q$ T T T F F T F F

• 2.
Construct a truth table for the following:
a)
$p$ ˅ ~$q$

b)
~$p$ ˄ $q$

• 3.
Truth Tables with Negations, Conjunctions, and Disjunctions (three statements)

Fill in the truth tables:

a)
 $p$ $q$ $r$ ~$p$ ~$p$ ˅ $q$ (~$p$ ˅ $q$) ˄ $r$ T T T T T F T F T F T T T F F F F T F T F F F F

b)
 $p$ $q$ $r$ ~$p$ ~$q$ ~$p$ ˄ ~$q$ (~$p$ ˄ ~$q$) ˅ $r$ T T T T T F T F T F T T T F F F F T F T F F F F

c)
 $p$ $q$ $r$ ~$p$ ~$r$ ~$p$ ˅ ~$r$ (~$p$ ˅ ~$r$) ˄ $q$ T T T T T F T F T F T T T F F F F T F T F F F F

• 4.
Construct a truth table for the following:
a)
$p$ ˅ $q$ ˅ $r$

b)
$p$ ˄ $q$ ˄ $r$