proof that contrapositive statement is logically equivalent to original statementSomethingRelatedToContrapositive2003-06-19 01:33:392007-09-06 23:06:25Proofcontrapositive0% this is the default PlanetMath preamble. as your knowledge
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% define commands hereYou 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.