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Set Theory and Predicate Calculus?

  1. Oct 21, 2009 #1
    Set Theory and Predicate Calculus (12 points)
    Given: P ⊆ Q
    Q ⊆ (S ∩ T)
    S ⊆ (R ∪ T^c)
    x(sub)1 ∈ P
    Use predicate calculus to prove x(sub)1 ∈ R.

    Studying for a test but I don't have this worked out for me. I honestly don't even know where to start. I know what union, intersect, etc and all the symbols mean I'm just bad at the Predicate Calculus.
  2. jcsd
  3. Oct 22, 2009 #2
    I think you need help from someone who knows that particular textbook.
  4. Oct 22, 2009 #3
    Oh really its that specific? :( too bad
  5. Oct 22, 2009 #4


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    Gold Member

    Nah, I might be able to help. I will look at it after class.

    Why not start by drawing a picture (e.g., a Venn diagram) to see what a model of these sentences must look like? I find that pictures are especially helpful at suggesting proofs by contradiction.
  6. Oct 22, 2009 #5


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    Science Advisor

    If [itex]x_1\in P[/itex] then, by the first line, [itex]x_1\in Q[/itex]. By the second line [itex]x_1\in S[/itex] and in T. By the third line then, [itex]x_1\in R[/itex] or [itex]x_1\in T^c[/itex]. But since [itex]x_1\in T[/itex], it can't be in [itex]T^c[/itex]. Therefore [itex]x_1\in R[/itex].

    Now all you have to do is express that in predicate calculus!
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