The two relations reflexive and identity 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
Let us consider an example to understand the difference between the two relations reflexive and identity.
Let A = {1, 2, 3}.
Let R_{1} and R_{2} be two relations defined on set A such that
R_{1} = {(1,1), (2,2), (3,3), (1,2)}
R_{2} = {(1,1), (2,2), (3,3)}
When we look at R_{1}, every element of A is related to itself and also, the element 1 is related to a different element 2.
More details about R_{1} :
(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 R_{1} is reflexive relation.
When we look at R_{2}, 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 R_{2} :
(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 R_{2} is identity relation.
That is,
Reflexive : Every element is related to itself
Identity : Every element is related to itself only
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