Definition:Inclusion Ordered Set

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Definition

Let $\left({S, \preceq}\right)$ be an ordered set.


$\left({S, \preceq}\right)$ is inclusion ordered set if and only if

$\mathord\preceq = \mathord\subseteq \cap \left({S \times S}\right)$


That means,

$\forall x, y \in S: x \preceq y \iff x \subseteq y$


Sources