Set definition

I think they're looking for X = {s such that s in S_alpha for all alpha in I} etc. Also, the hint is not helpful.

This question was asked before and this was (almost) the answer given - so I took my answer from that accepted solution.

We've had this problem before - what hint can you give on a definition? I can't think of one and haven't been able to think of one since we started...

I would believe that this stated answer would receive full marks on an exam...