\begin{definition}[Definition:Inverse of Subset/Group]
Let $\struct {G, \circ}$ be a group.
Let $X \subseteq G$.
Then the '''inverse''' of the subset $X$ is defined as:
:$X^{-1} = \set {x \in G: x^{-1} \in X}$
or equivalently:
:$X^{-1} = \set {x^{-1}: x \in X}$
\end{definition}