Question

For an integer n, a student states the following:
I. If $n$ is odd, $(n+1{)}^2$ is even
II. If $n$ is even, $(n-1{)}^2$ is odd
III. If $n$ is even, $n-1$ is even.
Which of the above statements would be true?

• A. I and III
• B. I and II
• C. I, II and III
• D. II and III

Answer 1

The correct option is B I and II

I. - If $n$ is odd, then $n+1$ is even, which implies that ${(n+1)}^2$ is even
II. - If $n$ is even, then $n-1$ is odd, which implies that ${(n-1)}^2$ is odd.
III - If n is even, then n-1 is not even. So it is false.

Hence, I and II are the two true statements.