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Reflexive but Not Symmetric Relation on {1,2,3} | JEE

JEE Maths question with a full step-by-step solution.

Question
The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\} on the set A={1,2,3}A = \{1, 2, 3\} is:
AReflexive but not symmetriccorrect
BReflexive but not transitive
CSymmetric and transitive
DNeither symmetric nor transitive
Solution
(1,1),(2,2),(3,3)∈R⇒R(1, 1), (2, 2), (3, 3) \in R \Rightarrow R is reflexive. (1,2)∈R(1, 2) \in R but (2,1)∉R⇒R(2, 1) \notin R \Rightarrow R is not symmetric. (1,2),(2,3)∈R⇒(1,3)∈R(1, 2), (2, 3) \in R \Rightarrow (1, 3) \in R, so the chain closes ⇒R\Rightarrow R is transitive. ∴R\therefore R is reflexive but not symmetric. Correct answer: (1)
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