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Math Help - Help Proving This Set-Based Theorem

  1. #1
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    Help Proving This Set-Based Theorem

    Greetings,
    I'm not sure how in-depth this community goes into discrete math (also, as far as I know discrete math varies depending on the school and location) but I'm having trouble proving this theorem.

    S x T subset S x U /\ S =! 0set implies T subset U

    where x is any arbitrary set operator, and /\ is and.

    Thanks.. Hope I supplied enough information.
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  2. #2
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    Re: Help Proving This Set-Based Theorem

    Quote Originally Posted by RobertXIV View Post
    where x is any arbitrary set operator, and /\ is and.
    Are you sure x is not Cartesian product?
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  3. #3
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    Re: Help Proving This Set-Based Theorem

    Indeed, emakarov is correct. Sorry about that one :P.
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  4. #4
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    Re: Help Proving This Set-Based Theorem

    Then do you need further help with this problem?
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  5. #5
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    Re: Help Proving This Set-Based Theorem

    Any member of S X T is of the form (s, t) where x \in S and t \in T. If that is a subset of S X ( U \cap S) then t \in S.
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  6. #6
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    Re: Help Proving This Set-Based Theorem

    I take it you mean s is an element of S, not x, correct?
    If so, this helps.
    Thank you!
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  7. #7
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    Re: Help Proving This Set-Based Theorem

    Quote Originally Posted by RobertXIV View Post
    I take it you mean s is an element of S, not x, correct?
    If so, this helps.

    I think that the problem is: If \left( {S \times T} \right) \subseteq \left( {S \times U} \right) \wedge S \ne \emptyset then T \subseteq U

    If T=\emptyset then T \subseteq U else suppose that t\in T.

    Given that (\exists s\in S) so (s,t)\in\left( {S \times T} \right)\subseteq\left( {S \times U} \right).

    Thus because this meams that t\in U. this shows that T \subseteq U.
    Last edited by Plato; April 1st 2013 at 03:23 PM.
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