
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

Re: Contrapositive proof
Do I understand correctly that you need to prove $\displaystyle \neg(P\land Q)$ and you want to prove $\displaystyle \neg P\lor\neg Q$ instead? Then yes, to prove a disjunction, it is sufficient to prove one of the disjuncts.