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Need set notation help.

  1. Nov 9, 2011 #1
    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[itex]\in[/itex]S : [itex]\exists[/itex]y[itex]\in[/itex]x, y[itex]\in[/itex]W}

    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.
  2. jcsd
  3. Nov 9, 2011 #2


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

    [tex]\{ (x, y) \in S \mid x \in W \vee y \in W \}[/tex]

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