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American footballs and Rugby balls are both considered 'balls' but neither are spheres.
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).
No. All it needs is one counter example to disprove: 6 is a multiple of 2 but NOT a multiple of 4.
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all spheres