It is almost NEVER okay to prove a statement with just an example. Certainly none of the statements proved above can be proved through an example. This is because in each of those cases we are trying to prove that something holds of all integers. We claim that \(n^2\) being even implies that \(n\) is even, no matter what integer \(n\) we pick. Showing that this works for \(n = 4\) is not even close to enough.
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