1. 0 and 1 (duality: 0 -- 1, · -- +)
X + 0 = X, X · 1 = X
X + 1 = 1, X · 0 = 0
2. Idempotent
X + X = X, X · X = X
3. Involution
(X')' = X
4. Complementarity
X + X' = 1, X · X' = 0
5. Commutative
X + Y = Y + X, X · Y = Y · X
6. Associative
(X + Y) + Z = X + (Y + Z) = X + Y + Z
(X · Y) · Z = X · (Y · Z) = X · Y · Z
7. Distributive
X · (Y + Z) = X · Y + X · Z
X + (Y · Z) = (X + Y) · (X +Z)
8. Simplification
X · Y + X · Y' = X, (X + Y) · (X + Y') = X
X + X · Y = X, X · (X + Y) = X
9. Multiplying and factoring
(X + Y) · (X' + Z) = X · Z + X' · Y
X · Y + X' · Z = (X + Z) · (X' + Y)
10. Consensus
X · Y + Y · Z + X · Z = X · Y + X' · Z
(X + Y) · (Y + Z) · (X' + Z) = (X + Y) · (X' + Z)
11. DeMorgan's law
(X + Y + Z + ...)' = X' · Y' · Z' · ...
(X · Y · Z · ...)' = X' + Y' + Z' + ...
{f(X1, X2, ..., Xn, 0, 1, +, ·)}' = {f(X1', X2', ..., Xn', 1, 0, ·, +)}
12. Duality
(X + Y + Z + ...)D = X · Y · Z · ...
(X · Y · Z)D = X + Y + Z + ...
{f(X1, X2, ..., Xn, 0, 1, +, ·)}D = f(X1', X2', ..., Xn', 1, 0, ·, +)