Question

Provide a counterexample to the following statement: if n² > 0, then n > 0?

Answer 1

A counterexample to the statement "if n² > 0, then n > 0" is n = -1. Squaring -1 gives 1, which is greater than 0, but -1 is not greater than 0.

Step-by-step explanation:

You asked for a counterexample to the statement "if n² > 0, then n > 0." A counterexample demonstrates that a statement is not always true. In this case, consider the number n = -1. When we square -1, we get (-1)² = 1 which is greater than 0. However, -1 is not greater than 0. This proves that the original statement is not true because there exists at least one instance (-1 in this case) where n² > 0, yet n is not greater than 0.