# Definition Given a [[Relation]] $\sim$ on a [[set]] $X$, $\sim$ is said to be an *equivalence relation* on $X$ if it obeys the following properties: 1. *Reflectivity:* $a \sim a$ 2. *Symmetry:* $a \sim b \iff b \sim a$ 3. *Transitivity:* $a \sim b \wedge b \sim c \implies a \sim c$ where $a,b,c \in X$. Equivalence relations lead to the partition of the set into [[Equivalence Class|equivalence classes]].