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Thread: 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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    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 $\displaystyle \mathcal{P}(A \cap B) \subseteq \mathcal{P}(A) \cap \mathcal{P}(B)$ and $\displaystyle \mathcal{P}(A) \cap \mathcal{P}(B) \subseteq \mathcal{P}(A \cap B)$

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

    i leave the other direction to you
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