Write the relationship as reflexive, symmetric and transitive to check whether the properties satisfy the relationship.
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.
has the same birthday as
Let's examine the relationship.
Property
Expression of Property
Relationship
Result
Reflexive
a=a
A has the same birthday as A.
Reflexive property satisfies the relationship.
Symmetric
If a=b, then b=a.
If A has the same birthday as B, then B has the same birthday as A.
Symmetric property satisfies the relationship.
Transitive
If a=b and b=c, then a=c.
If A has the same birthday as B and B has the same birthday as C, then A has the same birthday as C.
Transitive property satisfies the relationship.
As a result the relationship is reflexive, symmetric and transitive. Therefore, we can say that it is an equivalence relation.
