CMSC 201 -- Boolean Laws

Boolean Laws

Commutative laws:
x && y == y && x
x || y == y || x
Associative laws:
(x && y) && z == x && (y && z)
(x || y) || z == x || (y || z)
Identity laws:
1 && x == x
0 || x == x
Double negation:
!(!x) == x
Null laws:
0 && x == 0
1 || x == 1
Distributive laws:
x && (y || z) == (x && y) || (x && z)
x || (y && z) == (x || y) && (x || z)
Inverse laws:
x && !x == 0
x || !x == 1 && !y
Idempotent laws:
x && x == x
x || x == x
Absorption laws:
x && (x || y) == x
x || (x && y) == x
DeMorgan's laws:
!(x && y) == !y || !x
!(x || y) == !x && !y