Question

Determine the validity of the following statement: "For any integer n, if the square of n is an odd number, then n must be odd."A) TrueB) FalseC) Cannot be determinedD) Depends on specific values of n.

Answer 1

The statement is true because the square of an even number is even and the square of an odd number is odd, so if n squared is odd, then n must be odd.

Step-by-step explanation:

The statement "For any integer n, if the square of n is an odd number, then n must be odd" is TRUE. This is because when an even number is squared, the result is always even, and when an odd number is squared, the result is always odd. We can demonstrate this with a proof-by-contradiction by assuming that n is even – meaning n can be written as 2k (where k is an integer) – and then showing that the square would be 4k2, which is still even, contradicting the initial statement that the square is odd.