Power Set of Group under Induced Operation is Semigroup

Theorem
Let $\struct {G, \circ}$ be a group.

Let $\struct {\powerset G, \circ_\PP}$ be the algebraic structure consisting of the power set of $G$ and the operation induced on $\powerset G$ by $\circ$.

Then $\struct {\powerset G, \circ_\PP}$ is a semigroup.