COMEDK 2025 Evening Solved Paper

Concept:An equivalence relation on a set is one that is reflexive, symmetric, and transitive.Explanation:The given relation is $R = \{(1,1), (2,2), (3,3)\}$ on the set $\{1,2,3\}$.Check reflexivity: For every $x \in \{1,2,3\}$, the pair $(x,x)$ belongs to $R$. Since all three are present, $R$ is reflexive.Check symmetry: Whenever $(x,y) \in R$, the reversed pair $(y,x)$ must also be in $R$. All pairs are of the form $(x,x)$, so each reversed pair is the same and is present; thus $R$ is symmetric.Check transitivity: Whenever $(x,y) \in R$ and $(y,z) \in R$, the pair $(x,z)$ must be in $R$. Again, only diagonal pairs exist, so any such composition yields $(x,x)$, which is in $R$; therefore $R$ is transitive.Since $R$ satisfies all three properties, it is an equivalence relation.Answer:Option B – an equivalence relation.