If a relation $R$ on set $A=\{1,2,3\}$ is defined as $R=\{(1,1),(2,2),(3,3)\}$, what type of relation is $R$?

Solution

1. The set $A$ is $\{1,2,3\}$.
2. The relation $R$ contains exactly the pairs $(a,a)$ for every $a\in A$.
3. This is the definition of the identity relation on $A$.
4. Hence the answer is (C).