Is Your Set Builder Notation Correct for Describing Pairs in Sets S and W?

[ektrules]

Ok, I'm not very familiar with set notation. I was just wondering if the following is correct notation and means what I think:

{x\inS : \existsy\inx, y\inW}

S is a set of pairs of symbols (tuples of length 2 is the technical term I believe). W is a set of symbols.

What I want is the set of pairs in S that contain at least 1 symbol from set W.

Does my set builder notation correctly describe what I'm looking for? I don't necessarily have to use set builder notation; I just can't think of a way to describe it with unions, intersections, and quantifiers.

 

[CompuChip]

I think it is correct, however it may become slightly clearer if you explicitly write down the pairs:

\{ (x, y) \in S \mid x \in W \vee y \in W \}

If you would like to omit the set builder notation, you could consider something like
(W \times X) \cup (X \times W)
where X is the set of all symbols (and W \subseteq X).