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Math Help - Power Set Proofs

  1. #1
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    Power Set Proofs

    Can anyone please help me prove P(AnB) = P(A) n P(B)
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  2. #2
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    Quote Originally Posted by rookie23 View Post
    Can anyone please help me prove P(AnB) = P(A) n P(B)

    Maybe you can use the distributive laws .
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by mathaddict View Post
    Maybe you can use the distributive laws .
    for power sets?!

    Quote Originally Posted by rookie23 View Post
    Can anyone please help me prove P(AnB) = P(A) n P(B)
    we can prove this by showing that \mathcal{P}(A \cap B) \subseteq \mathcal{P}(A) \cap \mathcal{P}(B) and \mathcal{P}(A) \cap \mathcal{P}(B) \subseteq \mathcal{P}(A \cap B)

    For the first, assume X \in \mathcal{P}(A \cap B). then X \subseteq (A \cap B), but that means X \subseteq A and X \subseteq B, and thus we have X \in \mathcal{P}(A) and X \in \mathcal{P}(B) respectively. and so X \in \mathcal{P}(A) \cap \mathcal{P}(B)

    i leave the other direction to you
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