Albeit simple method :

These all the truth tables give us our first as albeit simple method for proving a theorem: where check whether it can be written in propositional logic and, so if it is a tautology, after then it must be true. Just because for instance, but if we were asked to prove this theorem from number theory look like: 

However we knew that this is a tautology, and that our number theory theorem fits in the tautology so let X represent the proposition sigma(n)=n, and so on, thus we identify that the theorem must be true, and regardless of what tau and sigma mean. So as an exercise, it shows that this is indeed a tautology, through using a truth table.

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