COMEDK · Maths · 20. Sets and Relations
The relation \(R=\{(1,1),(2,2),(3,3)\}\) on the set \(\{1,2,3\}\) is
- A reflexive only
- B an equivalence relation
- C transitive only
- D symmetric only
Answer & Solution
Correct Answer
(B) an equivalence relation
Step-by-step Solution
Detailed explanation
Let \(A = \{1, 2, 3\}\) and \(R = \{(1, 1), (2, 2), (3, 3)\}\). A relation \(R\) is reflexive if \((a, a) \in R\) for all \(a \in A\). Since \((1, 1), (2, 2), (3, 3) \in R\), the relation is reflexive. A relation \(R\) is symmetric if \((a, b) \in R \implies (b, a) \in R\). For…
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