Question

Use a counterexample to show that the following statement is false. The opposite of a number is never positive.

Short answer

The statement 'The opposite of a number is never positive' is false. A counterexample is -5, because its opposite is 5, which is positive.

Step-by-step solution

Identify the Problem

The problem statement asserts that 'the opposite of a number is never positive.' To disprove this we need a counter example, which is an example that violates the conditions of the statement.

Find a Counterexample

To find a counterexample of a number whose opposite is positive, we take a negative number. For instance, let's take the number -5. The opposite of -5 is 5, which is a positive number.

Conclude the reasoning

Since we have found a number (-5) whose opposite is positive (5), this is a counterexample that proves the statement 'the opposite of a number is never positive' is false.