Given a function $f : A → B$, let $R$ be the relation defined on $A$ by $aRa′$ whenever $f(a) = f(a′)$. Prove that $R$ is an equivalence relation and determine the equivalence classes.
To prove that $R$ is an equivalence relation, I know I have to show that R is reflexive, symmetric, and transitive. And from there, I can also determine the equivalence classes. However, I'm not sure where exactly to start. What exactly is the relation?