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Disproof by Counterexample

Disproof is the opposite of proof – instead of showing that something is true, we must show that it is false. Any statement that makes inferences about a set of numbers can be disproved by finding just one example for which it does not work.



Example 1

Disprove by counterexample that for any a,b\in{\mathbb Z}, if a^2=b^2, then a=b.


Example 2

Prove or disprove the statement that all prime numbers are odd.