Minimum closure of F (functional dependencies) help

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Homework Statement



F = {S -> NOPQZVWX, NX -> UV, NXT -> RY, YQ -> NXR, QZ -> S, PQ -> S}

Find the minimum closure of F.

Homework Equations



none

The Attempt at a Solution



So far I have made RHS of each FD into a single attribute and then I eliminated redundant attributes from LHS.

This is what I got. Is it correct so far? Do I still have to delete more stuff? I don't know what to do with QZ -> S and PQ -> S in terms of if they should be removed or not.

{NX -> U, NX -> V, S -> N, S -> O, S -> P, S -> Q, S -> Z, S -> V, S -> W, S -> X, NXT -> Y, QZ -> S, PQ -> S, YQ -> N, YQ -> X}
 

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