# Boolean algebra

Law | Equation |
---|---|

Annulment | A ^ 0 = 0, A v 1 = 1 |

Identity | A ^ 1 = A, A v 0 = A |

Idempotent | A v A = A, A ^ A = A |

Complement | A v A’ = 1, A ^ A’ = 0 |

Double Negation | (A’)’ = A |

De Morgan’s | (A ^ B)’ = A’ v B’, (A v B)’ = A’ ^ B’ |

Associative | (A v B) v C = A v (B v C), (A ^ B) ^ C = A ^ (B ^ C) |

Commutative | A v B = B v A, A ^ B = B ^ A |

Distributive | A ^ (B v C) = (A ^ B) v (A ^ C) |

Absorptive | A v (A^B) = A, A ^ (A v B) = A |

Consensus | AB v A’C v BC = AB v A’C |

Consensus | (A+B).(A’+C).(B+C) = (A+B).(A’+C) |

simplification of boolean algebra^{ᛦ}