Using the words necessary and sufficient rewrite the statement The integer `n` is odd if and only if `n^2` is odd Also check whether the statement is true.

Explanation

To rewrite the statement "The integer \( n \) is odd if and only if \( n^2 \) is odd" using the words "necessary" and "sufficient," we can break it down as follows:

1. **Understanding the Statement**: The phrase "if and only if" indicates a biconditional relationship between two statements:
- Let \( p \): "The integer \( n \) is odd."
- Let \( q \): "\( n^2 \) is odd."

The statement can be expressed as \( p \iff q \), meaning both \( p \) implies \( q \) and \( q \) implies \( p \).

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