counterexample

Everyday

(maths, logic) A counterexample is one example that shows a general statement is false. tree →

In the lessons

In maths and reasoning lessons, to test a claim like All prime numbers are odd, you look for a counterexample: 2 is prime and even, so the claim is false. One counterexample is enough to prove a statement wrong, but examples alone cannot prove it true. In everyday arguments, a counterexample answers someone who says always or never.

Examples

• 2 is a counterexample to the claim that all primes are odd. tree →
• Can you find a counterexample to Every square is a rectangle? (There is none.) tree →
• One counterexample shows the rule is false. tree →
• A penguin is a counterexample to All birds can fly. tree →
• She found a counterexample and won the argument. tree →
• Find a counterexample: All numbers ending in 9 are prime. (Answer: 9 itself.) tree →

Note

Countable, one word (sometimes counter-example). In maths, one counterexample proves a statement false; but many examples cannot prove it true for all numbers. Statements with all, every, always, never are tested this way.