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Math Help - Cross Products and Set Unions Proof

  1. #1
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    Cross Products and Set Unions Proof

    I'm hoping this is the right category, since it's set theory. If it's not I'll move it if someone knows a better place for these questions

    Prove that A X (B1U B2) = (A X B1) U (A X B2)

    I am actually stuck on the B1 B2 in this problem. It's some notation aspect that is keeping me from understanding what the problem is asking for. Are B1 and B2 separate sets?
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  2. #2
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    Re: Cross Products and Set Unions Proof

    Quote Originally Posted by renolovexoxo View Post
    Are B1 and B2 separate sets?
    Yes, B1 and B2 are arbitrary sets. The problem is asking to prove that A x (B U C) = (A x B) U (A x C) for arbitrary sets A, B, C.
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  3. #3
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    Re: Cross Products and Set Unions Proof

    Quote Originally Posted by renolovexoxo View Post
    I'm hoping this is the right category, since it's set theory. If it's not I'll move it if someone knows a better place for these questions

    Prove that A X (B1U B2) = (A X B1) U (A X B2)
     \begin{align*}(x,y)\in A\times (B\cup C)&\text{if and only if }x\in A\text{ and }y\in (B\cup C)  \\&\text{if and only if }x\in A\text{ and }(y\in B\text{ or }y\in C) \\&\text{if and only if }[x\in A\text{ and }(y\in B)]\text{ or }[ x\in A\text{ and }(y\in C))] \\&\text{if and only if }(x,y)\in(A\times B)\text{ or }(x,y)\in(A\times C)\end{align*}
    Last edited by Plato; August 27th 2012 at 03:09 PM.
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