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Math Help - Cartesian Product Formula Check

  1. #1
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    Cartesian Product Formula Check

    The question is to check if the following are true or not. When the set operations only include \cup \cap and -, I usually draw a ven diagram, but that doesn't seem to help much for the cartesian product... what's the best way to try to tackle problems like the following

    1. (A\times B)\subset (C\times D)\Rightarrow A\subset C and B\subset D



    2. (A\times B)\subset (C\times D)\Rightarrow A\subset C and B\subset D assuming A and B are not empty

    I seem to think both are true, so I'm not sure why in the second one we put the restriction on A and B



    **** I now see that if we let B be empty, then the product of A and B has to be a subset of the product of C and D, but A would not have to be a subset of C...
    Last edited by artvandalay11; September 3rd 2009 at 05:14 PM. Reason: figured it out
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