There are many symmetries in the operations AND (often written
or not written, since it is a multiplication operation) and OR
shown 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. |
