A relation $R$ on set $A = \{1, 2, 3\}$ is defined as $R = \{(1,1),(2,2),(3,3),(1,2),(2,1)\}$. Then $R$ is:

Step-by-step Solution:

Reflexive: $(1,1),(2,2),(3,3) \in R$ ✓

Symmetric: $(1,2) \in R \Rightarrow (2,1) \in R$ ✓

Transitive: $(1,2) \in R$ and $(2,1) \in R \Rightarrow (1,1) \in R$ ✓

Since $R$ is reflexive, symmetric, and transitive, it is an Equivalence Relation.

Hence, Option B is correct.