Write the relationship as reflexive, symmetric and transitive to check whether the properties satisfy the relationship.
It is not an equivalence relation.
Practice makes perfect
An equivalence relation is any relationship that satisfies the Reflexive, Symmetric, and Transitive Properties. Based on this definition, we will determine whether the given relation is an equivalence relation.
is bluer than
Let's examine the relationship.
Property
Expression of Property
Relationship
Result
Explanation
Reflexive
a=a
Cerulean is bluer than Cerulean.
Reflexive property does not satisfy the relationship.
Cerulean cannot be bluer than itself.
Symmetric
If a=b, then b=a.
If Cerulean is bluer than Azure, then Azure is bluer than Cerulean.
Symmetric property does not satisfy the relationship.
Azure cannot be bluer than Cerulean.
Transitive
If a=b and b=c, then a=c.
If Cerulean is bluer than Azure and Azure is bluer than Cornflower, then Cerulean is bluer than Cornflower.
Transitive property satisfies the relationship.
As a result the relationship is only transitive. Therefore, it is not an equivalence relation.
