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Math Help - Set Theory : Help Needed Plz

  1. #1
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    Set Theory : Help Needed Plz

    How Can I Prove That :

    1 - A Is a Subset Or Equal To P(A)
    2- P(A/\B) = P(A) /\ P(B)

    WHRE A AND B ARE SETS
    /\ IS INTERSECTION
    Thanks FOR THE HELP IN ADVANCE
    Last edited by KOXKOXKOX; March 13th 2008 at 08:29 AM. Reason: NO RIGHT
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  2. #2
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    You must redo your posting!
    Read it again. It is impossible for A to equal P(A).
    What is B? What does /\ mean?
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  3. #3
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    Quote Originally Posted by Plato View Post
    You must redo your posting!
    Read it again. It is impossible for A to equal P(A).
    What is B? What does /\ mean?
    /\ MEANS INTERSECTION
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  4. #4
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    Please answer the whole question.
    What is B?
    Do you mean A is a subset of B or of P(B)?
    As it is, the question is not yet clear.
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  5. #5
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    Quote Originally Posted by Plato View Post
    Please answer the whole question.
    What is B?
    Do you mean A is a subset of B or of P(B)?
    As it is, the question is not yet clear.
    THANK YOU FOR ANSWERING

    I HAVE TO Prove That :

    given any set A, then i have to prove that
    A Is a Subset Or Equal To P(A)

    given any 2 sets A and B , then i have to prove that
    2- P(A/\B) = P(A) /\ P(B)


    /\ IS INTERSECTION
    Thanks FOR THE HELP IN ADVANCE
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  6. #6
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    Well #1 is FALSE.
    The power set of A, P(A), is the collection of all subsets of A.
    Now it is true A \in P(A) because A \subseteq A.
    But cannot happen that A \subseteq P(A).

    #2 is simply a matter of noting that A \cap B \subseteq A\quad \& \quad A \cap B \subseteq B.
    X \in P\left( {A \cap B} \right)\quad  \Rightarrow \quad X \subseteq A \cap B
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