# Definition:Inverse of Subset/Group

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## Definition

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:

$X^{-1} = \set {x^{-1}: x \in X}$