Truth Tables
What is the difference between method and device? A method
is a device which you used twice.
—
George Polyá (1887–1985)
Truth tables
are used to list all possible truth values for a type of proposition.
|
p |
q |
|
|
T |
T |
T |
|
T |
F |
F |
|
F |
T |
F |
|
F |
F |
F |
|
p |
q |
|
|
T |
T |
T |
|
T |
F |
T |
|
F |
T |
T |
|
F |
F |
F |
|
p |
~p |
|
T |
F |
|
F |
T |
Example.
Construct a truth table for
Since we need to consider all
possible truth values for the proposition which has three simple propositions,
we need to consider 23 = 8 possibilities. We will also build from
the three simple propositions to the complete compound proposition.
|
p |
q |
r |
~q |
|
|
|
T |
T |
T |
F |
T |
T |
|
T |
T |
F |
F |
T |
F |
|
T |
F |
T |
T |
T |
T |
|
T |
F |
F |
T |
T |
F |
|
F |
T |
T |
F |
F |
F |
|
F |
T |
F |
F |
F |
F |
|
F |
F |
T |
T |
T |
T |
|
F |
F |
F |
T |
T |
F |
Equivalency,
Tautology, and Contradiction
