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.