## You are here

Homecontrapositive

## Primary tabs

# contrapositive

Given an implication of the form

$p\implies q$ |

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

$\neg q\implies\neg p$ |

(“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.

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

03B05*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff