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Math Help - Cartesian Proof Sets

  1. #1
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    Cartesian Proof Sets

    Prove:

    A B = ∅ if and only if A = ∅ or B = ∅.
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  2. #2
    MHF Contributor kalagota's Avatar
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    maybe this will help you..
    |A\times B| = |A|\cdot |B|
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jacob233 View Post
    Prove:

    A B = ∅ if and only if A = ∅ or B = ∅.
    i would do this by proving the forward direction using the contrapositive, and the converse via a direct proof.

    at some point in your text you should have it written that A \times \emptyset = \emptyset for every set A. this should help you prove the converse directly.

    for the forward direction, assume NOT A = \emptyset or B = \emptyset. then by DeMorgan's laws, we have that A \ne \emptyset AND B \ne \emptyset. now if both A and B are nonempty, what can you say about A \times B?
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  4. #4
    MHF Contributor kalagota's Avatar
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    here is another hint: it should be trivial that  |A| = 0 \Longleftrightarrow A=\emptyset

    use this hint and the previous hint i posted and you shall have the (two way) proof i am thinking..
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