Surjective prove

**tukilala** · December 13th 2008, 11:36 AM

A={1,2,3,4,5}
f :P(A)→P(A), f (X ) =A\X.
how can i prove that this function is Surjective???

**Plato** · December 13th 2008, 12:02 PM

Suppose that $M \in P(A)$ .
Now note that:
$\begin{array}{rcl} {A\backslash \left( {A\backslash M} \right)} & = & {A \cap \left( {A \cap M^c } \right)^c } \\ {} & = & {A \cap \left( {A^c \cup M} \right)} \\ {} & = & {A \cap M} \\ {} & = & M \\ \end{array}$ .

**tukilala** · December 13th 2008, 12:17 PM

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

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Surjective prove

can u explain me please

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