Question: Questions about a Family of Subsets

Hi, someone help please. How I can fix the following problem (preferably avoiding for-loops as they are too slow):

From a family of subsets (say) S={{a,b},{a,b,c},{b,c},{c}} of the set X={a,b,c}
1). Extract all the subsets i.e. members of S, which have 'a' as their member?
2). For any (a,b) in X x X, check if 'a' is member of all those subsets which have 'b' also as their member or not?

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