# proof that contrapositive statement is logically equivalent to original statement

You can see that the contrapositive of an implication^{} is true by considering
the following:

The statement $p\Rightarrow q$ is logically equivalent to $\mathrm{\neg}p\vee q$ which can also be written as $\overline{p}\vee q$.

By the same token, the contrapositive statement $\overline{q}\Rightarrow \overline{p}$ is logically equivalent to $\mathrm{\neg}\overline{q}\vee \overline{p}$ which, using double negation on $q$, becomes $q\vee \overline{p}$.

This, of course, is the same logical statement.

Title | proof that contrapositive statement is logically equivalent to original statement |
---|---|

Canonical name | ProofThatContrapositiveStatementIsLogicallyEquivalentToOriginalStatement |

Date of creation | 2013-03-22 13:42:10 |

Last modified on | 2013-03-22 13:42:10 |

Owner | sprocketboy (2515) |

Last modified by | sprocketboy (2515) |

Numerical id | 10 |

Author | sprocketboy (2515) |

Entry type | Proof |

Classification | msc 03B05 |

Related topic | Inverse7 |

Related topic | Inverse6 |