Symmetric Difference with Intersection forms Ring

Theorem
Let $S$ be a set.

Let:
 * $\symdif$ denote the symmetric difference operation
 * $\cap$ denote the set intersection operation
 * $\powerset S$ denote the power set of $S$.

Then $\struct {\powerset S, \symdif, \cap}$ is a commutative ring with unity, in which the unity is $S$.

This ring is not an integral domain.

Also see

 * Symmetric Difference with Union does not form Ring