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theEric

  • 3 years ago

Math proof help, please! Relations and subsets involved. I don't see the solution! My math book proved that if sets \[A, B,C,D\] existed such that \[A \subseteq C \]and\[B \subseteq D\] then \[(A \times B) \subseteq (C \times D)\] I need to show that the converse of that is false. I think the converse is\[(A \times B) \subseteq (C \times D)\]implies\[A \subseteq C \]and\[B \subseteq D\]. But I can't understand how it is false for some group of sets \[A,B,C,D\].

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  1. zugzwang
    • 3 years ago
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    Use null sets :)

  2. theEric
    • 3 years ago
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    Alright, thanks.. I never went into writing a proof on that, but I thought about it and didn't see it working... Thank you!

  3. zugzwang
    • 3 years ago
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    No problem :)

  4. theEric
    • 3 years ago
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    Ah!! I think I finally see it.. Thanks for making me concentrate more on the null set issue!

  5. theEric
    • 3 years ago
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    Woo!

  6. zugzwang
    • 3 years ago
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    Got it? :)

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