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Math Help - 30 minute set theory

  1. #1
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    30 minute set theory

    1. if X is a set, find X\cap P(X)

    I think it's X but I don't know how to show it

    2. if P(X) = P(Y), is necessarily X + Y justify your answer
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  2. #2
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    X = \left\{ {a,b} \right\}\,\& \,P(X) = \left\{ {\emptyset ,\{ a\} ,\{ b\} ,\{ a,b\} } \right\}
    Is there a single element in both of those sets?

    As for #2. I have no idea what X+Y could mean.
    In the last century older mathematicians such as R L Moore used it to mean union. Is that the case here?
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  3. #3
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    oops I just held the shift button
    it's X = Y
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  4. #4
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    Quote Originally Posted by jbpellerin View Post
    it's X = Y
    t \in X \Rightarrow \left\{ t \right\} \in P(X) = P(Y) \Rightarrow t \in Y \Rightarrow X \subseteq Y
    Now you finish it.
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