Currently I am trying to understand the equivalence class from the Herstein's book. And I am facing problem to understand the concept and also can't understand the theorem given in the page number 8. Book name is Topics in algebra, second edition.
Theorem 1.1.1. The distinct equivalence classes of an equivalence relation on $A$ provide us with a decomposition $o$f A as a union of mutually disjoint subsets. Conversely, given a decomposition of $A$ as a union of mutually disjoint, nonempty subsets, we can define an equivalence relation on $A$ for which these subsets are the distinct equivalence classes.