Properties of Equivalence

The equivalence operator should have 3 properties:

• reflexive
• symmetric
• transitive An operator is an equivalence operator if and only if it fits all 3 properties.

Properties of equivalence relations

Reflexive

An item is equal to itself $A=A$

Symmetric

The order in which items are compared do not affect the final result If: $A=B$ Then: $B=A$

Transitive

Equivalent items are interchangeable. If: $A=B$ And $B=C$ Then $A=C$ As long as the compared items have a common equivalent, the compared items are equivalent.