Equivalence Relation

Definition

A Binary Relation $\sim$ on a set $X$ is called an equivalence relation on $X$ if it satisfies the following properties for all $a,b,c\in X$:

1. Reflexive
2. Symmetric
3. Transitive

Equivalence Class

The set of elements in $X$ that are equivalent to a specific element under the relation $\sim$ is called the equivalence class. For example, the equivalence class of an element $a$ is denoted as follows. $[a]=\{x\in X:x\sim a\}$