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contrapositive (Definition)

Given an implication of the form

$\displaystyle p \implies q$
(“p implies q”) the contrapositive of this implication is
$\displaystyle \neg q \implies \neg p$
(“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: equivalent, implication
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This is version 5 of contrapositive, born on 2001-11-16, modified 2005-04-11.
Object id is 891, canonical name is Contrapostive.
Accessed 9661 times total.

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

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