Let P, Q, and R be sentences, each of which is true or false (and none of which is both). The two truth tables below shows that "and" distributes over "or". To be specific, "P or (Q and R)" means the same thing as "(P or Q) and (P or R)". In the arithmetic of real numbers, this is similar to the rule that a*(b+c)=(a*b)+(a*c).

P | Q | R | Q and R | P or (Q and R) |
---|---|---|---|---|

T | T | T | T | T |

T | T | F | F | T |

T | F | T | F | T |

T | F | F | F | T |

F | T | T | T | T |

F | T | F | F | F |

F | F | T | F | F |

F | F | F | F | F |

P | Q | R | P or Q | P or R | (P or Q) and (P or R) |
---|---|---|---|---|---|

T | T | T | T | T | T |

T | T | F | T | T | T |

T | F | T | T | T | T |

T | F | F | T | T | T |

F | T | T | T | T | T |

F | T | F | T | F | F |

F | F | T | F | T | F |

F | F | F | F | F | F |