\begin{definition}[Definition:Operation Induced on Quotient Set]
Let $\struct {S, \circ}$ be an algebraic structure.
Let $\RR$ be a congruence relation on $\struct {S, \circ}$.
Let $S / \RR$ be the quotient set of $S$ by $\RR$.
The '''operation $\circ_\RR$ induced on $S / \RR$ by $\circ$''' is defined as:
:$\eqclass x \RR \circ_\RR \eqclass y \RR = \eqclass {x \circ y} \RR$
\end{definition}