Long integers can be used to represent subsets of an n-element set, for n up
to n=15 (Why?). Single number k corresponds to long integer 
, the set 
is
represented by 
, etc.
If S, T are integers representing sets, then S AND T represents the intersection of sets, S OR T is the union, and S AND NOT T is the difference of sets.
To check if 
, verify if 2^j AND T is non-zero.