## Symmetries in Boolean Algebra

There are many symmetries in the operations AND (often writtenor not written, since it is a multiplication operation) and ORshown in the following table.

These symmetries make boolean algebra easier to manipulate and boolean expression easier to simplify.

Example:

Simplify:

 Expression Rule(s) Used Original Expression Distributive. Complement, Identity. Commutative, Distributive. Associative, Idempotent. Distributive. Idempotent, Identity, Distributive. Identity, twice.