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Thread: Cartesian Product Formula Check

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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 $\displaystyle \cup \cap$ 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. $\displaystyle (A\times B)\subset (C\times D)\Rightarrow A\subset C$ and $\displaystyle B\subset D$



    2. $\displaystyle (A\times B)\subset (C\times D)\Rightarrow A\subset C$ and $\displaystyle B\subset D$ 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; Sep 3rd 2009 at 05:14 PM. Reason: figured it out
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