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.