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.
â‰
Let's examine the relationship.
Property
Expression of Property
Relationship
Result
Explanation
Reflexive
a=a
a ≠a
Reflexive property does not satisfy the relationship.
a is always equal to itself.
Symmetric
If a=b, then b=a.
If a≠b, then b≠a.
Symmetric property satisfies the relationship.
Transitive
If a=b and b=c, then a=c.
If a≠b and b≠c, then a≠c.
Transitive property may satisfy the relationship.
There is not enough information to guarantee that the relationship is satisfied as it is still possible that a=c.
As a result the relationship is not reflexive and potentially not transitive. Therefore, it is not an equivalence relation.
