# Contrapositive proof

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• Feb 16th 2013, 07:16 AM
jojo7777777
Contrapositive proof
Having a contrapositive proof in which negation was done by DeMorgan's law, http://upload.wikimedia.org/math/d/0...9ee2cd8e7e.png.
Would it be correct to say that in some proofs just one of the cases, ~P or ~Q is true? If so, would it be enough to stop proving when one of the cases was shown to be true?

Thanking you in anticipation
• Feb 16th 2013, 08:07 AM
emakarov
Re: Contrapositive proof
Do I understand correctly that you need to prove $\neg(P\land Q)$ and you want to prove $\neg P\lor\neg Q$ instead? Then yes, to prove a disjunction, it is sufficient to prove one of the disjuncts.