Definition:Inverse of Subset/Group

Definition
Let $\left({G, \circ}\right)$ be a group.

Let $X \subseteq G$.

Then the inverse of the subset $X$ is defined as:
 * $X^{-1} = \left\{{x \in G: x^{-1} \in X}\right\}$

or equivalently:
 * $X^{-1} = \left\{{x^{-1}: x \in X}\right\}$