CMSC 201 -- 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