# 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**

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)}

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