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Math Help - proof involving power sets, and intersection

  1. #1
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    proof involving power sets, and intersection

    Power set of (A intersect B)=Power set of A intersect the power set of B

    x is an element of D which is an element of the power set of (A intersect B). a subset of A and B must contain elements that are in both A and B so x must be an element of A and B. Since x is an element of A it must be contained in the power set of A and since x is in B it must also be in the power set of B

    i think this wrong but im not sure how to fix it
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by leinadwerdna View Post
    Power set of (A intersect B)=Power set of A intersect the power set of B

    x is an element of D which is an element of the power set of (A intersect B). a subset of A and B must contain elements that are in both A and B so x must be an element of A and B. Since x is an element of A it must be contained in the power set of A and since x is in B it must also be in the power set of B

    i think this wrong but im not sure how to fix it
    Nope, looks right to me.

    All you need to do is point out that the argument reverses.

    Here's the thing proved in symbols:

    Intersection of Power Sets - ProofWiki
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  3. #3
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    An element of a Set a is an element of a subset of the powerset

    Note the given wiki proof more carefully. Although x is an element of A intersection B, it is not an element of the power set of either nor their intersection. It is an element of a subset of the power set, yes, but not an element of the power set itself. A power set is a set containing all possible subsets of a given set. This really is confusing though, I know. The same concept can be applied in reverse in that although x is an element of the power set of a set, it is not an element of the set itself.
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