# Definition:Dual Relation/Complement of Inverse

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## 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:

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

where:

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