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NCERT Class 12 · Ch 1 Miscellaneous Exercise · Q6

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Miscellaneous Exercise Question 6

On A={1,2,3}, how many relations containing (1,2),(1,3) are reflexive and symmetric but not transitive?

💡 Concept Hints

  1. Add the forced diagonal and reverse pairs first; only then inspect the remaining choices.
  2. Write the defining condition carefully and preserve every domain restriction while simplifying.

✅ Step-by-Step Solution

Final Answer: A: 1.
  1. Reflexivity forces (1,1),(2,2),(3,3); symmetry forces (2,1),(3,1). Together with the two given pairs these form a seven-pair relation R₀.
  2. The only remaining pairs are (2,3),(3,2). Symmetry allows either neither or both, so there are two possible reflexive symmetric relations.
  3. R₀ is not transitive: (2,1),(1,3) belong but (2,3) does not. Adding both remaining pairs gives A×A, which is transitive.
  4. Exactly one relation meets the requirement, so choose A.

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