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Math Help - Help with Cartesian product of power sets please

  1. #1
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    Question Help with Cartesian product of power sets please

    I hope I'm not breaking any rules by posting this, but just came across a homework problem that I was unsure on.
    What is the Cartesian product of A and the power set of B if A={1} and B={}?
    I know that the Cartesian product of A x B under these cases is the empty set, but it's not the same thing.
    So far I've tried looking at it a few different ways: {1} x {{}}= ? being one
    Thank you

    PS: I'm new here so please be gentle
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  2. #2
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    Re: Help with Cartesian product of power sets please

    Quote Originally Posted by chuciulla93 View Post
    So far I've tried looking at it a few different ways: {1} x {{}}= ? being one

    \{1\}\times\{\emptyset\} has one element. What is the ordered pair?
    Last edited by Plato; November 25th 2012 at 04:32 AM.
    Thanks from chuciulla93
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    Re: Help with Cartesian product of power sets please

    Would it be: { (1,{}), ({},1) } ?
    Please see my edit.
    And yes the pair is (1,\emptyset}).
    Last edited by Plato; November 25th 2012 at 04:35 AM.
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    Re: Help with Cartesian product of power sets please

    Thank you
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    Re: Help with Cartesian product of power sets please

    Quote Originally Posted by chuciulla93 View Post
    Please see my edit.
    And yes the pair is (1,\emptyset}).
    I want to explain my edit. Frankly my first reaction was to the title "Cartesian product of power sets please"
    But upon rereading the post, that was not being asked.

    But was it actually what was meant?
    The power set \mathcal{P}(\emptyset)=\{\emptyset\}

    The power set \mathcal{P}(\{1\})=\{\emptyset,~\{1\}\}

    Therefore \mathcal{P}(\{1\})\times \mathcal{P}(\emptyset)=\{(\emptyset,\emptyset),~ ( \{ 1\},\emptyset)\}: that is two elements.
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