3 deleted 95 characters in body
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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: 1. (false, false, false), 2. (true, false, false), 3. (true, true, false), 4. (true, true, true).

So there1 and 4 are the 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.  

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.  

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.

2 added 19 characters in body
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If X is true, then a necessary condition N must be true. If
If N is false, then X must be false. 

If a sufficient condition S is true, then X is true. If
If X is false thwn, 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.

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.

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.

1
source | link

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.