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proof by contradiction


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A direct proof of a statement q is a logically correct argument establishing the truth of q. A proof by contradiction assumes that q is false and derives the truth of some statement r and of its negation ¬r. This contradiction shows that the initial assumption cannot hold, hence establishing the truth of q. A more complicated example is a proof that ‘if p then q’. A proof by contradiction assumes that p is true and that q is false, and derives the truth of some statement r and of its negation ¬r. This contradiction shows that the initial assumptions cannot both hold, and so a valid proof has been given that, if p is true, then q is true.

Subjects: Mathematics.


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