# Boolean Algebra

• Invented by George Boole
• Functions only take 0 or 1 as input

## Laws

PropertyAndOr
CommutativeAB = BAA + B = B + A
Associative(AB)C = A(BC)(A + B) + C = A + (B + C)
DistributiveA(B + C) = (AB) + (AC)A + (BC) = (A + B)(A + C)
IdentityA1 = AA + 0 = A
NullA0 = 0A + 1 = 1
IdempotencyAA = AA + A = A
Involution(A')' = A(A')' = A
ComplementA(A') = 0A + (A') = 1
De Morgan's Law(AB)' = A' + B'(A + B)' = A'B'