## 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. |