Boolean Algebra
- Invented by George Boole
- Functions only take
0or1as input
Laws
| Property | And | Or |
|---|---|---|
| Commutative | AB = BA | A + B = B + A |
| Associative | (AB)C = A(BC) | (A + B) + C = A + (B + C) |
| Distributive | A(B + C) = (AB) + (AC) | A + (BC) = (A + B)(A + C) |
| Identity | A1 = A | A + 0 = A |
| Null | A0 = 0 | A + 1 = 1 |
| Idempotency | AA = A | A + A = A |
| Involution | (A')' = A | (A')' = A |
| Complement | A(A') = 0 | A + (A') = 1 |
| De Morgan's Law | (AB)' = A' + B' | (A + B)' = A'B' |