Consider the additive monoid of natural numbers and calculate the congruence generated by $\{(2,3)\}$. I know the answer is that the congruence has 3 classes which are $\{0\}$, $\{1\}$, and the rest.
Also I have been given the definition that the congruence on $A$ generated by a set $R$ is the smallest congruence on $A \times A$ which contains $R$.
So if anybody could help tell me how the answer was calculated that would really be appreciated.