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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, then 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.