UIL CS Boolean Identities

Idempotent Law for OR

A + A = A

Idempotent Law for AND

A * A = A

Commutative Law for OR

A + B = B + A

Commutative Law for AND

A * B = B * A

Associative Law for OR

A + (B + C) = (A + B) + C

Associative Law for AND

A * (B * C) = (A * B) * C

Distributive Law for AND over OR

A * (B + C) = A * B + A * C

Distributive Law for OR over AND

A + B * C = (A + B) * (A + C)

Law of Union

A + 1 = 1

Law of Intersection

A * 0 = 0

Law of Absorption AND

A * (A + B) = A

Law of Absorption OR

A + A * B = A

Identity Law for AND

A * 1 = A

Identity Law for OR

A + 0 = A

Double Negative Law

!!A = A

Law of Complement for OR

A + !A = 1

Law of Complement for AND

A * !A = 0

Demorgan’s Law OR

!(A + B) = !A * !B

Demorgan’s Law AND

!(A * B) = !A + !B

Exclusive OR (XOR)

A ^ B = A * !B + !A * B = !A * B + A * !B

Exclusive NOR (XNOR)

!(A ^ B) = A * B + !A * !B

Law of the disappearing opposite

A + !A * B = A + B

FOIL

(A + B) * (C + D) = A * C + A * D + B *C + B* D