File:Necessary and sufficient venn (set) diagram.svg

Summary

The necessary and sufficient conditions in the language of sets (Venn diagrams). Necessary condition means that in order to get into the sufficient area, S, you must at first enter the necessary area, N. Sufficient condition means that being in S ensures that you are in the N. Necessary and sufficient (if and only if) condition means that S = N. In this case, if you are in one then you are in the other and if you not in one, they you are not in the other. Whatever, you can only either be outside both, in N or in both. It is impossible to be in S but not in N. This way, sufficient condition S "implies" N. Therefore, material implication has 3 true values for possible configurations and one false for impossible S and not N.

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