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. |