5-5 Indirect Proof

Objective

To use indirect reasoning to write proofs

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In the Solve It, you can conclude that a square must contain a certain number if you can eliminate the other three numbers as possibilities. This type of reasoning is called indirect reasoning. In indirect reasoning, all possibilities are considered and then all but one are proved false. The remaining possibility must be true.

Essential Understanding You can use indirect reasoning as another method of proof.

A proof involving indirect reasoning is an indirect proof. Often in an indirect proof, a statement and its negation are the only possibilities. When you see that one of these possibilities leads to a conclusion that contradicts a fact you know to be true, you can eliminate that possibility. For this reason, indirect proof is sometimes called proof by contradiction.

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