It is an example that demonstrates, by its very existence, that an assertion is false. Usually experience suggests that the assertion is true: there is a large amount of supporting "evidence" but the statement has not been proven. The counter-example, though demolishes the assertion
For example:
Assertion: all prime numbers are odd.
Counter example: 2. It is a prime but it is not odd.
Therefore the assertion is false.
This was a favourite "trap" at GCSE exams in the UK.
Assertion: if you divide a nuber it becomes smaller.
Counter example 1: 2 divided by a half is, in fact, 4.
Counter example 2: -10 divided by 2 is -5 (which is larger by being less negative).
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