Boolean Laws and Simplification

Front

A + 0 = A and A · 1 = A

Back

Identity Law

Front

A + A = A and A · A = A

Back

Idempotent Law

Front

A + A' = 1 and A · A' = 0

Back

Complement Law

Front

A'' = A

Back

Double Negation Law

Front

A + B = B + A and A · B = B · A

Back

Commutative Law

Front

(A + B) + C = A + (B + C) and (A · B) · C = A · (B · C)

Back

Associative Law

Front

A · (B + C) = A · B + A · C

Back

Distributive Law

Front

A + (A · B) = A and A · (A + B) = A

Back

Absorption Law

Front

(A · B)' = A' + B' and (A + B)' = A' · B'

Back

De Morgan's Theorem

Front

A + A' · B = A + B

Back

Law of common identities