There might be statements which really cannot be rephrased as implications. For example, “\(\sqrt 2\) is irrational.” In this case, it is hard to know where to start. What can we assume? Well, say we want to prove the statement \(P\text{.}\) What if we could prove that \(\neg P \imp Q\) where \(Q\) was false? If this implication is true, and \(Q\) is false, what can we say about \(\neg P\text{?}\) It must be false as well, which makes \(P\) true!
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