\begin{definition}[Definition:Power Structure]
Let $\struct {S, \circ}$ be an algebraic structure.
Let $\powerset S$ denote the power set of $S$.
Let $\circ_\PP$ denote the operation induced on $\powerset S$ by $\circ$ as follows:
:$\forall A, B \in \powerset S: A \circ_\PP B = \set {a \circ b: a \in A, b \in B}$
Then the resulting algebraic structure $\struct {\powerset S, \circ_\PP}$ is called the '''power structure of $\struct {S, \circ}$'''.
\end{definition}