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Math Help - prove equal sets

  1. #1
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    prove equal sets

    I have this problem as homework, I don't think they're equal, but i need to prove it. Any body can help?
    " If X and Y are sets and it is known that the collection of subsets of X equals the collection of Subsets of Y, can one conclude that X=Y?"
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by vavi View Post
    I have this problem as homework, I don't think they're equal, but i need to prove it. Any body can help?
    " If X and Y are sets and it is known that the collection of subsets of X equals the collection of Subsets of Y, can one conclude that X=Y?"
    I think they are equal

    My Observation: Define the set to be the union of all the singleton subsets. Now proving X=Y should be easy.
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