Let A = { 1, 2, 3 } and consider the relation R = { (1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}.
Then R is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → reflexive but not symmetric
R is tested for each of the three properties in turn.
Reflexive: (1, 1), (2, 2) and (3, 3) are all in R, so R is reflexive.
Symmetric: (1, 2) ∈ R but (2, 1) ∉ R, so R is not symmetric.
Transitive: Apart from pairs of the form (a, a), which never break transitivity, the only chain (a, b), (b, c) with a ≠ b ≠ c is (1, 2), (2, 3), and it needs (1, 3), which is in R. So R is transitive.
Hence R is reflexive and transitive but not symmetric, which is Option (3).
NCERT Exemplar:
Relations and Functions
