Identity Relation

Identity relation : Let A be a set. Then the relation I$_{A}$= {(a,a): a $\in $ A} on A is called the identity-relation on A.
In other words, a relation I$_{A}$ on A is called the identity-relation if every element of A is related itself only.
I$_{A}$: A $\rightarrow $ A Where I$_{A}$(x)= x

For example : If A = {1,2,3}, then the relation I$_{A}$ ={(1,1),(2,2),(3,3)} is the identity-relation on set A.
But If we add (1,3) and (3,2) ordered pair in the set then it will not be an identity-relation.

Examples on Identity Relation

Example 1: Let A = {7,8,9}, write the identity-relation set for set A.
 Solution : As we know that if A be a set. Then the relation
I$_{A}$= {(a,a): a ∈ A} So
A = {7,8,9} $\Rightarrow$ I$_{A}$= {(7,7),(8,8),(9,9)}

 Example 2: Let A = {2,3,4}, write the identity-relation set for set A.
 Solution : As we know that if A be a set. Then the relation
I$_{A}$= {(a,a): a ∈ A} So
A = {2,3,4} $\Rightarrow$ I$_{A}$= {(2,2),(3,3),(4,4)}
12th grade math

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