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Math Help - relation between power sets

  1. #1
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    relation between power sets

    Suppose that A and B are not disjoint sets. How is, P(A instersect B), the power set of A intersect B, related to P(A) intersect P(B)? Provide evidence for this conclusion.


    I just...I have no idea what this is asking or how to figure it out.
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  2. #2
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    Quote Originally Posted by kiddopop View Post
    Suppose that A and B are not disjoint sets. How is, P(A instersect B), the power set of A intersect B, related to P(A) intersect P(B)? Provide evidence for this conclusion.
    \mathcal{P}(A\cap B)=\mathcal{P}(A)\cap\mathcal{P}(B)
    You must show that X\in\mathcal{P}(A\cap B) if and only if X\in(\mathcal{P}(A)\cap\mathcal{P}(B)).
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  3. #3
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    Quote Originally Posted by Plato View Post
    \mathcal{P}(A\cap B)=\mathcal{P}(A)\cap\mathcal{P}(B)
    You must show that X\in\mathcal{P}(A\cap B) if and only if X\in(\mathcal{P}(A)\cap\mathcal{P}(B)).
    how do i do that? i'm so lost.
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  4. #4
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    Quote Originally Posted by kiddopop View Post
    how do i do that? i'm so lost.
    What does X\in\mathcal{P}(A\cap B) mean?
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  5. #5
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    Quote Originally Posted by Plato View Post
    What does X\in\mathcal{P}(A\cap B) mean?
    that x is an element of the power set of A and B?
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  6. #6
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    Quote Originally Posted by kiddopop View Post
    that x is an element of the power set of A and B?
    What does it mean to be a an element of the power set of A intersect B?
    Let's say T\in\mathcal{P}(S), then what does that imply about T~\&~S.

    Now use your textbook to give a full answer.
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