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 taller than
Let's examine the relationship.
Property
Expression of Property
Relationship
Result
Explanation
Reflexive
a=a
A is taller than A.
Reflexive property does not satisfy the relationship.
A cannot be taller than herself/himself.
Symmetric
If a=b, then b=a.
If A is taller than B, then B is taller than A.
Symmetric property does not satisfy the relationship.
B cannot be taller than A.
Transitive
If a=b and b=c, then a=c.
If A is taller than B and B is taller than C, then A is taller than C.
Transitive property satisfies the relationship.
As a result the relationship is only transitive. Therefore, it is not an equivalence relation.
