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If X is true, then a necessary condition N must be true. If N is false then X must be false. If a sufficient condition S is true then X is true. If X is false thwn S must be false.

The possible combinations for N, X and S are: (false, false, false), (true, false, false), (true, true, false), (true, true, true).

So there are two cases where N is not the opposite of S: If the necessary condition N, the sufficient condition S, and X itself are all three false, or all three true.