If a relation R is defined on the set X = {1,2,3,4} as R = {(1,1),(2,2),(3,4),(4,3)}, then R is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → symmetric and not reflexive.
Checking each property on X = {1, 2, 3, 4}:
Reflexive: needs (1, 1), (2, 2), (3, 3) and (4, 4) in R. (3, 3) is not in R, so R is not reflexive.
Symmetric: (3, 4) and (4, 3) are both in R, and (1, 1), (2, 2) are their own reverses. So R is symmetric.
Transitive: (3, 4) and (4, 3) are in R, so (3, 3) would have to be in R. It is not, so R is not transitive.
So R is symmetric, not reflexive and not transitive. Of the options, only “symmetric and not reflexive” is true: options (1) and (3) call R reflexive or transitive, and option (4) says R is not symmetric.