SOLUTION: Show that if x^2 is odd, x is odd. Use proof by contradiction.

Question 992554: Show that if x^2 is odd, x is odd. Use proof by contradiction.
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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Show that if x^2 is odd, x is odd. Use proof by contradiction.
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We are given that is odd.
We need to prove that x is odd.

Let us assume that x is not odd. Then x is even. In other words, x is divisible by 2. Hence, x = 2n, where n is integer.

Then = = is even.

This contradicts to the fact that is odd, which is given.

The source of the contradiction is the assumption that x is not odd.

Hence, x is odd.

The proof is completed.

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