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# 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*

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