Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability (resit) / 2 / a / Solution

A binary relation $R$ on $A$ is an equivalence relation exactly when it is reflexive, symmetric, and transitive:The equivalence class of $a\in A$ is $[a{]}_R=\{b\in A:aRb\}$. The equivalence classes partition $A$: every element belongs to its own class, and two classes are either equal or disjoint.