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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- Dec 13th 2008, 11:36 AMtukilalaSurjective 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??? - Dec 13th 2008, 12:02 PMPlato
Suppose that $\displaystyle M \in P(A)$.

Now note that:

$\displaystyle \begin{array}{rcl}

{A\backslash \left( {A\backslash M} \right)} & = & {A \cap \left( {A \cap M^c } \right)^c } \\

{} & = & {A \cap \left( {A^c \cup M} \right)} \\

{} & = & {A \cap M} \\

{} & = & M \\

\end{array} $. - Dec 13th 2008, 12:17 PMtukilalacan u explain me please
why u did

A/A/M

???

why not A/ just ones? why twice?