DIFFERENCE BETWEEN REFLEXIVE AND IDENTITY RELATION

About "Difference between reflexive and identity relation"

"What is the difference between reflexive and identity relation?" is a big question having had by the students who study math in both school level and college level. 

The reason for why they have such a big question is, both reflexive and identity relation appear as if they were same. But there is a huge difference between them. 

The difference between reflexive and identity relation can be described in simple words as given below.

Reflexive = " Every element is related to itself "

Identity   = " Every element is related to itself only "

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".

Very few websites explain the difference between the reflexive relation and identity relation. Even though those websites explain the difference, students find it difficult to understand it. We consider all these factors and give a detailed explanation for difference between reflexive relation and identity relation with an example. The example given above clearly illustrates the difference between reflexive relation and identity relation.




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