Chapter 6.3, Problem 8WE

To determine

To write: an indirect proof for $n$ is oddin paragraph form.

Explanation of Solution

Given information:

  $n$ is an integer and $n^2$ is odd.

Calculation:

An indirect proof is initiated by assuming temporarily that the conclusion above is untrue and then work from there to finally conclude that the assumption is untrue.

Proof:

Assume temporarily that $n$ is not odd.

Therefore, $n$ is even

If this were true, then $n^2$ will be even

However, it is given that $n^2$ is odd.

Hence, our initial assumption that $n$ is odd is not true.

Hence, $n$ is odd.