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To prove: If n^2 is odd, then n is odd. In the following statements, first...

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To prove: If n^2 is odd, then n is odd.

In the following statements, first, determine whether a statement shall be used in the proof, then, if the statement shall be used, determine the right sequence to present it.

Assume that n is even.

Assume that n is odd.

n^2 is even

n = 2k+1 for an integer k.

n^2 = (2k+1)^2 = 2(2k^2+2k) + 1.

proof

n = 2k for an integer k

Consider an arbitrary integer n

n^2 is odd.

n^2 = (2k)^2 = 2(2k).

QED

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