counterexample

«counterexample» in Mova's school dictionary: one example that shows a general statement is false — its meaning for a pupil, its sense in the lessons and examples.

part of speech

noun (a counterexample, counterexamples)

meaning for a pupil

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

sense 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.

Trees and pragmatics

Every meaning and example of «counterexample» parsed by Mova, each sentence with its dependency tree and frames.