## You are here

Homeproof that contrapositive statement is logically equivalent to original statement

## Primary tabs

# 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 $\neg p\vee q$ 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 $\neg\overline{q}\vee\overline{p}$ which, using double negation on $q$, becomes $q\vee\overline{p}$.

This, of course, is the same logical statement.

Related:

Inverse7, Inverse6

Major Section:

Reference

Type of Math Object:

Proof

Parent:

## 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

## Recent Activity

Jul 5

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias