\begin{definition}[Definition:Inverse Image]
Let <math>\mathcal{R} \subseteq S \times T</math> be a relation.
Let <math>\mathcal{R}^{-1} \subseteq T \times S</math> be the inverse relation to <math>\mathcal{R}</math>, defined as:
:<math>\mathcal{R}^{-1} = \left\{{\left({t, s}\right): \left({s, t}\right) \in \mathcal{R}}\right\}</math>
Let <math>D \subseteq T</math>.
The '''inverse image''' of <math>D</math> under <math>\mathcal{R}</math> is the set:
:<math>\left\{{s \in S: \mathcal{R} \left({s}\right) \in D}\right\}</math>
That is, the '''inverse image''' of <math>D</math> under <math>\mathcal{R}</math> is the image of <math>D</math> under <math>\mathcal{R}^{-1}</math>.
\end{definition}