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 conjunction distributes over alternation. To be specific, "P and (Q or R)" means the same thing as "(P and Q) or (P and R)".

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

T | T | T | T | T |

T | T | F | T | T |

T | F | T | T | T |

T | F | F | F | F |

F | T | T | T | F |

F | T | F | T | F |

F | F | T | T | F |

F | F | F | F | F |

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

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

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

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

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

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

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

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

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