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# Boolean Algebra

- Invented by George Boole
- Functions only take
`0`

or`1`

as input

## Laws

Property | And | Or |
---|---|---|

Commutative | AB = BA | A + B = B + A |

Associative | (AB)C = A(BC) | (A + B) + C = A + (B + C) |

Distributive | A(B + C) = (AB) + (AC) | A + (BC) = (A + B)(A + C) |

Identity | A1 = A | A + 0 = A |

Null | A0 = 0 | A + 1 = 1 |

Idempotency | AA = A | A + A = A |

Involution | (A')' = A | (A')' = A |

Complement | A(A') = 0 | A + (A') = 1 |

De Morgan's Law | (AB)' = A' + B' | (A + B)' = A'B' |