Power set/Ring structure with symmetric difference/Exercise

Let ${}M$ be a set. Show that the power set ${}{\mathfrak {P}}\,(M)$ is a commutative ring, if we consider the intersection ${}\cap$ as multiplication and the symmetric difference

${}A\triangle B={\left(A\setminus B\right)}\cup {\left(B\setminus A\right)}\,$

as addition (what are the neutral elements?).

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