The mathematics: Boolean algebra
A Boolean algebra consists of
- A set of elements B
- Binary operations {+ , �}
- A unary operation { ' }
And the following axioms:
1. The set B contains at least two elements, a, b, such that a ? b
2. Closure: a + b is in B a � b is in B
3. Commutative: a + b = b + a a � b = b � a
4. Associative: a + (b + c) = (a + b) + c a � (b � c) = (a � b) � c
5. Identity: a + 0 = a a � 1 = a
6. Distributive: a + (b�c)=(a + b)�(a + c) a�(b + c)=(a�b) + (a�c)
7. Complementarity: a + a' = 1 a � a' = 0