# Definition:Maximal/Relation

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## Definition

Let $\left({S, \mathcal R}\right)$ be a relational structure.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is an $\mathcal R$-maximal element of $T$ if and only if:

$\forall y \in T: x \not \mathrel {\mathcal R} y$