In this article , you will find common laws for preposition logic. These are very helpful in solving problems like simplifying a complex prepositional statement into a simple one. They also form the basis for arguments which you will learn in future lessons.

Identity Laws (1)

p | T | p and T |
---|---|---|

0 | 1 | 0 |

1 | 1 | 1 |

p | F | p or T |
---|---|---|

0 | 0 | 0 |

1 | 0 | 1 |

Domination Laws (2)

p | T | p or T |
---|---|---|

0 | 1 | 1 |

1 | 1 | 1 |

p | F | p and F |
---|---|---|

0 | 0 | 0 |

1 | 0 | 0 |

Idempotent Laws (3)

p | p | p or p |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

p | p | p and p |
---|---|---|

0 | 0 | 0 |

1 | 1 | 1 |

Double Negation Law (4)

p | not p | not (not p) |
---|---|---|

0 | 1 | 0 |

1 | 0 | 1 |

Commutative Laws (5)

p | q | p or q | q or p |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 0 | 1 | 1 |

1 | 1 | 1 | 1 |

p | q | p and q | q and p |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 1 | 0 | 0 |

1 | 0 | 0 | 0 |

1 | 1 | 1 | 1 |

Associative Laws (6)

p | q | r | p or q | q or r | (p or q) or r | p or (q or r) |
---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 1 | 1 | 1 | 1 |

0 | 1 | 1 | 1 | 1 | 1 | 1 |

1 | 0 | 0 | 1 | 0 | 1 | 1 |

1 | 0 | 1 | 1 | 1 | 1 | 1 |

1 | 1 | 0 | 1 | 1 | 1 | 1 |

1 | 1 | 1 | 1 | 1 | 1 | 1 |

Distributive Laws (7)

p | q | r | q and r | p or (q and r) | p or q | p or r | (p or q) and (p or r) |
---|---|---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |

0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |

1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |

1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |

1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

De Morgan’s Laws (8)

p | q | not p | not q | not(p or q) | not p and not q |
---|---|---|---|---|---|

0 | 0 | 1 | 1 | 1 | 1 |

0 | 1 | 1 | 0 | 0 | 0 |

1 | 0 | 0 | 1 | 0 | 0 |

1 | 1 | 0 | 0 | 0 | 0 |

p | q | not p | not q | not(p and q) | not p or not q |
---|---|---|---|---|---|

0 | 0 | 1 | 1 | 0 | 0 |

0 | 1 | 1 | 0 | 1 | 1 |

1 | 0 | 0 | 1 | 1 | 1 |

1 | 1 | 0 | 0 | 1 | 1 |

Absorption Laws (9)

p | q | p and q | p or (p and q) |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 1 | 0 | 0 |

1 | 0 | 0 | 1 |

1 | 1 | 1 | 1 |

p | q | p or q | p and (p or q) |
---|---|---|---|

0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 1 |

1 | 1 | 1 | 1 |

Negation Laws (10)

p | not p | p or not p |
---|---|---|

0 | 1 | T |

1 | 0 | T |

p | not p | p and not p |
---|---|---|

0 | 1 | F |

1 | 0 | F |