\begin{definition}[Definition:Equivalence Relation Induced by Partition]
Let $S$ be a set.
Let $\Bbb S$ be a partition of $S$.
Let $\RR \subseteq S \times S$ be the relation defined as:
:$\forall \tuple {x, y} \in S \times S: \tuple {x, y} \in \RR \iff \exists T \in \Bbb S: \set {x, y} \subseteq T$
Then $\RR$ is the '''(equivalence) relation induced by (the partition) $\Bbb S$'''.
\end{definition}