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: 1. (false, false, false), 2. (true, false, false), 3. (true, true, false), 4. (true, true, true). 

So 1 and 4 are the two cases where N is not the opposite of S.