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Class 12 Relations And Functions · Mcq Single Correct1 Markscounting_relations

Class 12 Maths · Relations And Functions · Mcq Single Correct #22

Let \(A=\{1,2,3\}\). Find the number of relations containing \((1,2)\) and \((1,3)\) which are reflexive and symmetric but not transitive.

✅ Step-by-Step Solution

Final Answer: Option (A): 1
  1. Reflexivity and symmetry force \(R_0=\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)\}\). This fails transitivity. The only other symmetric completion adds both \((2,3)\) and \((3,2)\), making it universal and transitive. Thus exactly one qualifies.

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