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Welcome to our Math lesson on Rejecting a Supposition by Counter Example, this is the sixth lesson of our suite of math lessons covering the topic of Identities, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Sometimes it is not worth trying to prove a supposition but it is enough to reject (disproof) it through a counter - example. Recall that a supposition must be always true to be accepted. If it is 1000 times true and only 1 time false, it is definitely regarded as false.
For example, if we claim that all odd numbers ending with 3 are prime, it is enough to find a counter - example (in this case, 33) to reject this claim. Let's consider an example to clarify this point better.
Disprove by counter - example the claim that the sum of four consecutive numbers is always odd.
We take for example 7, 8, 9 and 10. Adding them yields
Since this counter - example gave an even number as result, the original claim is false.
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