Find all items which are subsets of an item
Your problem is the same one faced by SAT solvers who want to eliminate subsumed clauses from a CNF formula.  Any clause $B$ that contains a superset of the literals of another clause $A$ in the formula is redundant and can be removed without changing the satisfiability of the formula.  We say $A$ subsumes $B$, so $B$ can be discarded.  Instead of single valued literals, you have these item tuples but it is the same problem as finding $A$.

The algorithms used are refinements of the naive algorithm, where you iterate through each element of a potential subset, checking to see if it occurs in $x$.
If you sort $x$'s items you can reduce the linear time search to log $\vert{x}\vert$.  If you use a hashtable to store $x$'s items you can have amortized constant time for each search.  Because of the hashing overhead, save this optimization for large sets.  Bitmask signatures for each set allow you to do a cheap initial check, only doing the expensive iteration and searching of $x$ if the bitmaps can't rule out a subset match.