Past exam of the year 1 of the computer science course of the University of Oxford / 2022 / Discrete mathematics, continuous mathematics, and probability / Discrete mathematics / 3 / c / ii

This binary relation is not an equivalence relation, because it is not symmetric: $(0,0)R(0,1)$ since $0\le 1$, but $(0,1)R(0,0)$ is false. In fact the injective encoding $(a,b)\mapsto 10a+b$ gives a total order. There are no equivalence classes for this binary relation.