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