The relation R in the set A = {1, 2, 3, 4} is given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)} is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Reflexive and transitive but not symmetric
Reflexive: (1, 1), (2, 2), (3, 3) and (4, 4) are all in R, so R is reflexive.
Symmetric: (1, 2) is in R but (2, 1) is not, so R is not symmetric.
Transitive: check every pair (a, b), (b, c) in R with a ≠ b and b ≠ c (pairs with a = b or b = c give nothing new):
(1, 3) and (3, 2) give (1, 2), which is in R
There is no other such chain: (1, 2) and (3, 2) end at 2, and from 2 the only pair is (2, 2). So R is transitive.
Hence R is reflexive and transitive but not symmetric (so it is not an equivalence relation).
NCERT (2026-27 edition):
Types of Relations
