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.

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