# Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Introduction/Logical Reasoning

< Mathematical Proof | Appendix | Answer Key1.1, Logical Reasoning.

These are the answers to the exercises in section 1.1, Logical Reasoning

- Truth tables

P | Q | ||
---|---|---|---|

T | T | F | T |

T | F | F | T |

F | T | T | T |

F | F | T | F |

P | Q | ||
---|---|---|---|

T | T | F | F |

T | F | T | T |

F | T | F | T |

F | F | T | T |

P | Q | R | ||
---|---|---|---|---|

T | T | T | T | T |

T | T | F | T | F |

T | F | T | T | T |

T | F | F | T | F |

F | T | T | T | T |

F | T | F | T | F |

F | F | T | F | T |

F | F | F | F | T |

P | Q | R | S | |||
---|---|---|---|---|---|---|

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

P | Q | R | S | |||
---|---|---|---|---|---|---|

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2. Negated statements