Relation/Examples/Subsets of Initial Segment of Natural Numbers

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Example of Relation

Let $S$ be the set of all the subsets of the initial segment of the natural numbers $\set {1, 2, 3, \ldots, n}$.

Let $\RR$ be the set defined as:

$\RR = \set {\tuple {S_1, S_2}: S_1 \subseteq S_2, S_1 \in S, S_2 \in S}$

Then $\RR$ is a relation on $S$.