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# counterexample

noun (a counterexample, counterexamples)

«counterexample» in the English dictionary: everyday — its meanings, how the lessons use it, and examples, each with its tree on Mova.

## Everyday

(maths, logic) A counterexample is one example that shows a general statement is false. [tree →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#m1)

### 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 →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#x1)
- Can you find a counterexample to Every square is a rectangle? (There is none.) [tree →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#x2)
- One counterexample shows the rule is false. [tree →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#x3)
- A penguin is a counterexample to All birds can fly. [tree →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#x4)
- She found a counterexample and won the argument. [tree →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#x5)
- Find a counterexample: All numbers ending in 9 are prime. (Answer: 9 itself.) [tree →](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/#x6)

### 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.

## On Mova

- [Trees and pragmatics of «counterexample» in the school dictionary](https://mova.elamur.ai/free/en/corpora/dictionaries/school/C/counterexample/): every meaning and example parsed by Mova, with its dependency tree and frames.
- [«counterexample» in the school dictionary](https://mova.elamur.ai/free/en/dictionaries/school/w/counterexample.html) on Mova free.