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contrapositive (Definition)

Given an implication of the form $$p \implies q$$ (``p implies q'') the contrapositive of this implication is $$\neg q \implies \neg p$$ (``not q implies not p'').

An implication and its contrapositive are equivalent statements. When proving a theorem, it is often more convenient or more intuitive to prove the contrapositive instead.




"contrapositive" is owned by yark. [ full author list (2) | owner history (1) ]
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proof that contrapositive statement is logically equivalent to original statement (Proof) by sprocketboy
examples of contrapositive (Example) by alozano
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Cross-references: theorem, equivalent, implication
There are 19 references to this entry.

This is version 5 of contrapositive, born on 2001-11-16, modified 2005-04-11.
Object id is 891, canonical name is Contrapostive.
Accessed 14593 times total.

Classification:
AMS MSC03B05 (Mathematical logic and foundations :: General logic :: Classical propositional logic)

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