Symmetric Difference on Power Set forms Abelian Group

Theorem
Let $$S$$ be a set such that $$\varnothing \subset S$$ (i.e. $$S$$ is not empty).

Let $$A * B$$ be defined as the symmetric difference between $$A$$ and $$B$$.

Let $$\mathcal P \left({S}\right)$$ be the power set of $$S$$.

Then the algebraic structure $$\left({\mathcal P \left({S}\right), *}\right)$$ is an abelian group.

Proof
From Power Set Closed under Symmetric Difference, we have that $$\left({\mathcal P \left({S}\right), *}\right)$$ is closed.

The result follows directly from Set System Closed with Symmetric Difference is Group.