Definition:Dual Relation/Inverse of Complement

Definition
Let $\mathcal R \subseteq S \times T$ be a binary relation.

Then the dual of $\mathcal R$ is denoted $\mathcal R^d$ and is defined as:


 * $\mathcal R^d := \left({\overline{\mathcal R}}\right)^{-1}$

where:
 * $\overline {\mathcal R}$ denotes the complement of $\mathcal R$
 * $\left({\overline{\mathcal R}}\right)^{-1}$ denotes the inverse of the complement of $\mathcal R$.