# 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.

Title proof that contrapositive statement is logically equivalent to original statement ProofThatContrapositiveStatementIsLogicallyEquivalentToOriginalStatement 2013-03-22 13:42:10 2013-03-22 13:42:10 sprocketboy (2515) sprocketboy (2515) 10 sprocketboy (2515) Proof msc 03B05 Inverse7 Inverse6