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[parent] proof that contrapositive statement is logically equivalent to original statement (Proof)

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.



"proof that contrapositive statement is logically equivalent to original statement" is owned by sprocketboy.
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See Also: inverse, inverse statement


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Cross-references: negation, logically equivalent, implication, contrapositive
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This is version 7 of proof that contrapositive statement is logically equivalent to original statement, born on 2003-06-19, modified 2007-09-06.
Object id is 4379, canonical name is SomethingRelatedToContrapositive.
Accessed 3847 times total.

Classification:
AMS MSC: 03B05 (Mathematical logic and foundations :: General logic :: Classical propositional logic)
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