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Math Help - P(A) interesect P(B)

  1. #1
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    P(A) interesect P(B)

    I wnat to prove that for an sets A and B, P(A) interesect P(B) is not equal to the null set. I know A is an element of P(A) and B is an elemnt of P(B), but where do I go from here?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by kathrynmath View Post
    I wnat to prove that for an sets A and B, P(A) interesect P(B) is not equal to the null set. I know A is an element of P(A) and B is an elemnt of P(B), but where do I go from here?
    \emptyset is a subset of any set
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    Quote Originally Posted by Jhevon View Post
    \emptyset is a subset of any set

    Yeah, I know that, but what would be a hint on doing the proof?
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    Quote Originally Posted by kathrynmath View Post
    Yeah, I know that, but what would be a hint on doing the proof?
    That is the proof.
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    Quote Originally Posted by Plato View Post
    That is the proof.
    Ok, so I say that the null set is a subset of P(A) and P(B). Wouldn't this imply that P(A) interesect P(B)= null set.
    I don't know...
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  6. #6
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    Quote Originally Posted by kathrynmath View Post
    Ok, so I say that the null set is a subset of P(A) and P(B). Wouldn't this imply that P(A) interesect P(B)= null set.
    I don't know...
    No indeed.
    \left\{ \emptyset  \right\} \ne \emptyset
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