Boolean Identities:

Complement Laws

x + ~x = 1 x · ~x = 0

Law of the Double Complement

~(~x) = x

Idempotent Laws

x + x = x x · x = x

Identity Laws

x + 0 = x x · 1 = x

Dominance Laws

x + 1 = 1 x · 0 = 0

Commutative Laws

x + y = y + x x · y = y · x

Associative Laws

x + (y + z) = (x + y) + z

x · (y · z) = (x · y) · z

Distributive Laws

x + (y · z) = (x + y) · (x + z)

x · (y + z) = (x · y)+(x · z)

DeMorgan's Laws

~(x · y) = ~x + ~y

~(x + y) = ~x · ~y

Absorption Laws

x · (x + y) = x

x + (x · y) = x

Simplification Laws

x · (~x + y) = x · y

x + (~x · y) = x + y

x · y + x · z + ~y · z = x · y + ~y · z