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Math Help - Surjective prove

  1. #1
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    Surjective prove

    A={1,2,3,4,5}
    f :P(A)→P(A), f (X ) =A\X.
    how can i prove that this function is Surjective???
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  2. #2
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    Suppose that M \in P(A).
    Now note that:
    \begin{array}{rcl}<br />
{A\backslash \left( {A\backslash M} \right)} & = & {A \cap \left( {A \cap M^c } \right)^c } \\<br />
{} & = & {A \cap \left( {A^c \cup M} \right)} \\<br />
{} & = & {A \cap M} \\<br />
{} & = & M \\<br />
\end{array} .
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  3. #3
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    can u explain me please

    why u did
    A/A/M
    ???
    why not A/ just ones? why twice?
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