Question

What is the difference between Identity relation and reflexive relation ?

Answer 1

Example for difference between reflexive and identity relation

Let us consider an example to have better understanding of the difference between the two relations. (Reflexive vs Identity)

Let A = {1, 2, 3}

Let R₁ and R₂ be two relations defined on set A such that

R₁ = { (1,1) , (2,2) , (3,3) , (1,2) }

R₂ = { (1,1) , (2,2) , (3,3) }

When we look at R₁ , every element of A is related to itself and also, the element "1" is related to a different element "2".

More details about R₁

(i) "1" is related to "1", "2" is related to "2" and "3" is related to "3"

(ii) Apart from "1" is related to "1", "1" is also related to "2"

Here we can not say that "1" is related to "1" only. Because "1" is related to "2" also.

This is the point which makes the reflexive relation to be different from identity relation.

Hence R₁ is reflexive relation

When we look at R₂, every element of A is related to it self and no element of A is related to any different element other than the same element.

More details about R₂

(i) "1" is related to "1", "2" is related to "2" and "3" is related to "3"

(ii) "1" is related to "1" and it is not related to any different element.

The same thing happened to "2" and "3".

(iii) From the second point, it is very clear that every element of R is related to itself only. No element is related to any different element

This is the point which makes identity relation to be different from reflexive relation.

Hence R₂ is identity relation

That is,

Reflexive = " Every element is related to itself "

Identity = " Every element is related to itself only "

From the example explained above, students would be able to understand the stuff "Difference between reflexive and identity relation".