Boolean Expression Simplification

Boolean expression simplification is the process of reducing a Boolean expression to its simplest form, while preserving its original meaning.
Here are the basic steps for simplifying Boolean expressions:
1. Apply the Idempotent Laws: a AND a = a, a OR a = a
2. Apply the Commutative Laws: a AND b = b AND a, a OR b = b OR a
3. Apply the Associative Laws: (a AND b) AND c = a AND (b AND c), (a OR b) OR c = a OR (b OR c)
4. Apply the Distributive Laws: a AND (b OR c) = (a AND b) OR (a AND c), a OR (b AND c) = (a OR b) AND (a OR c)
5. Eliminate Double Negations: NOT NOT a = a
6. Apply De Morgan's Laws: NOT (a AND b) = NOT a OR NOT b, NOT (a OR b) = NOT a AND NOT b
7. Simplify using the Absorption Laws: a AND (a OR b) = a, a OR (a AND b) = a