# contrapositive

Given an implication^{} of the form

$$p\u27f9q$$ |

(“p implies q”) the *contrapositive* of this implication is

$$\mathrm{\neg}q\u27f9\mathrm{\neg}p$$ |

(“not q implies not p”).

An implication and its contrapositive are equivalent^{} statements. When proving a theorem^{}, it is often more convenient or more intuitive to prove the contrapositive instead.

Title | contrapositive |
---|---|

Canonical name | Contrapositive |

Date of creation | 2013-03-22 11:59:17 |

Last modified on | 2013-03-22 11:59:17 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 9 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 03B05 |