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Math Help - Cartesian product of universal set.

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    Cartesian product of universal set.

    Hi, I don't know how to prove this.

    UXA^C = (UXA)^C

    What is the result of UxA? I know Ax= but have no idea about universal set. Thanks for any help.
    Last edited by truevein; November 6th 2010 at 12:37 PM.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by truevein View Post
    Hi, I don't know how to prove this.

    UXA^C = (UXA^C)

    What is the result of UxA? I know Ax= but have no idea about universal set. Thanks for any help.
    I believe you're trying to prove that U\times\left(U-A\right)=U-\left(U\times A\right). Is that right?
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    Really sorry about the displacement of the parenthesis, I corrected my question.
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    We know that \left( {\forall x} \right)\left[ {x \in U} \right], the universe.

    So if  (x,y)\in U\times A^c then because x\in U we know y\notin A so (x,y)\in (U\times A)^c.

    If (u,w)\in (U\times A)^c then u \notin U \vee w \notin A.
    Again we know that u\in U so w\notin A.
    So (u,w)\in U\times A^c.
    Last edited by Plato; November 6th 2010 at 02:12 PM.
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