Equivalence Relation

Definition

A binary Relation $\sim$ on set $X$ that satisfies the following conditions for all $a,b,c\in X$

• Reflective: $a\sim a$
• Symmetric: $a\sim b\Rightarrow b\sim a$
• Transitive: $a\sim b\wedge b\sim c\Rightarrow a\sim c$

Facts

The equivalence relation may be constructed from the Partition