Boolean Operations
Truth Tables
We can show the results of the boolean operators using
truth tables. Assume that
A and B
are boolean expressions:
A |
! A |
FALSE |
TRUE |
TRUE |
FALSE |
A |
B |
A && B |
FALSE |
FALSE |
FALSE |
FALSE |
TRUE |
FALSE |
TRUE |
FALSE |
FALSE |
TRUE |
TRUE |
TRUE |
|
A |
B |
A || B |
FALSE |
FALSE |
FALSE |
FALSE |
TRUE |
TRUE |
TRUE |
FALSE |
TRUE |
TRUE |
TRUE |
TRUE |
|
We can also show the results of more complex expressions using
truth tables. For example, assume that
A, B, and
C are boolean expressions:
A |
B |
C |
A || B |
(A || B) && C |
FALSE |
FALSE |
FALSE |
FALSE |
FALSE |
FALSE |
FALSE |
TRUE |
FALSE |
FALSE |
FALSE |
TRUE |
FALSE |
TRUE |
FALSE |
FALSE |
TRUE |
TRUE |
TRUE |
TRUE |
TRUE |
FALSE |
FALSE |
TRUE |
FALSE |
TRUE |
FALSE |
TRUE |
TRUE |
TRUE |
TRUE |
TRUE |
FALSE |
TRUE |
FALSE |
TRUE |
TRUE |
TRUE |
TRUE |
TRUE |
Alyce Brady, Kalamazoo College