What is Reflexive Relation?
A reflexive relation is a type of binary relation on a set where every element in the set is related to itself. In other words, for any element “a” in the set, the pair (a, a) is a part of the relation. Formally, a relation R on a set A is reflexive if, for all elements “a” in A, (a, a) is in R.
For example, the “is equal to” relation (denoted by “=”) is a reflexive relation on the set of real numbers, because every real number is equal to itself. Similarly, the “is a parent of” relation on the set of people is reflexive because every person is their own parent (in a biological sense).
Reflexive Relation Definition
A relation R on a set A is called a reflexive relation if
(a, a) ∈ R ∀ a ∈ A, i.e. aRa for all a ∈ A, where R is a subset of (A x A), i.e. the cartesian product of set A with itself.
Reflexive Relation Meaning
This means if element “a” is present in set A, then a relation “a” to “a” (aRa) should be present in the relation R. If any such aRa is not present in R then R is not a reflexive relation.
A reflexive relation is denoted as:
R = {(a, a): a ∈ A}
Example: Consider set A = {a, b} and R = {(a, a), (b, b)}. Here R is a reflexive relation as for both a and b, aRa and bRb are present in the set.
Reflexive Relations in Mathematics
Reflexive Relation is a mathematical or set-theoretical relation in which every element is related to itself, meaning that for every element ‘x’ in the set, the pair (x, x) is a part of the relation. Other than Reflexive, there are many types of relations such as Symmetric, Transitive, Identity, etc. In maths, relation is a subset of the cartesian product of a set with another set where some well-defined rule relates the elements of two sets with each other.
This article helps you learn about Reflexive Relation in detail including all the various subtopics such as Definition, Meaning, Properties of Reflexive Relation, etc. Other than that we will also learn how to verify any relation to be Reflexive Relation.
Table of Content
- What is Reflexive Relation?
- Examples of Reflexive Relations
- Properties of a Reflexive Relation
- How to verify a Reflexive Relation?’
- Reflexive Relation: Related Relation