Question

Which is a counterexample for the conditional statement?

If two positive numbers are multiplied together, then the product will be greater than both of the two positive numbers.

2 x 4
5 x (−3)

Answer 1

A counterexample must satisfy the hypothesis (both numbers positive) but make the conclusion false.

- 2 × 4 = 8 — this satisfies the hypothesis and the conclusion, so it is not a counterexample.
- 5 × (−3) = −15 — this does not satisfy the hypothesis (−3 is not positive), so it cannot be a counterexample.

Example of a valid counterexample: 1/2 × 1/2 = 1/4. Both factors are positive, but the product 1/4 is less than each factor, so the conditional statement is false.