1. Presented by: Tutorial Services The Math Center
Truth Tables
Presented by:
Tutorial Services
The Math Center

2. Truth Tables ~ ~p “And” p q “Or”
A truth table is a device used to determine when a compound statement is true or false.
Connectives used in truth tables:
Formal Name
Symbol
Read
Symbolic Form
Negation ~
“Not” ~p
Conjunction
“And”
p q
Disjunction
“Or”
Conditional
“If-then”
Bi-conditional
“If and only If”

3. Types of Arguments When finding the truth value of a
Conjunction
When finding the truth value of a
conjunction, all values must be true
in order for the entire conjunction to
be true.
For example, if p and q are true,
then (p  q) is true.
For example, if p is true and q is
false, (p  q) is false.
For example, if p and q are false,
then (p  q) is false. p q T F

4. Types of Arguments When finding the truth value of a
Disjunction
When finding the truth value of a
disjunction, only one value needs to
be true in order for the entire
disjunction to be true.
For example, if p is true and q is false,
then (p  q) is true.
For example, if both p and q are true,
For example, if both p and q are false,
then (p  q) is false. p q T F

5. Types of Arguments The truth values of ~p are exactly
Negation
The truth values of ~p are exactly
the opposite truth values of p.
For example, true for p would be
false for ~p.
For example, false for (p  q)
would be true for ~(p  q). p ~p T F

6. Types of Arguments When finding the truth value of a
Conditional
When finding the truth value of a
conditional statement, same values
will be true. Otherwise, follow the
truth value of the conclusion (which
is the second proposition).
For example, if p and q are false,
then (p  q) is true.
For example, if p is true and q is
false, then (p  q) is false.
For example, if p is false and q is
true, then (p  q) is true. p q
p q T F

7. Types of Arguments When finding the truth value of
Bi-conditional
When finding the truth value of
a bi-conditional statement, same
values will be true. Otherwise,
the truth value will be false.
For example, if both p and q are
false, then (p  q) is true.
For example, if p is true and q
is false, then (p  q) is false.
For example, if p is false and q
is true, then (p  q) is false. p q T F

8. Examples
Example1: p q
p  q ~q T F

9. Examples
Example 2: p q r ~r
q ~r T F

10. Examples
Example 3: p q r ~r
q ~r T F

11. Truth Tables Links
Truth Tables Handout