# Relation/Examples/Subsets of Initial Segment of Natural Numbers

Let $S$ be the set of all the subsets of the initial segment of the natural numbers $\set {1, 2, 3, \ldots, n}$.
Let $\mathcal R$ be the set defined as:
$\mathcal R = \set {\paren {S_1, S_2}: S_1 \subseteq S_2, S_1 \in S, S_2 \in S}$
Then $\mathcal R$ is a relation on $S$.