Let \(A = \{1, 2, 3\}\) and let R be the relation on A given by \(R = \{(1, 2)\}\). Then R is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → transitive but neither reflexive nor symmetric
Not reflexive: (1, 1) is not in R.
Not symmetric: (1, 2) is in R, but (2, 1) is not.
Transitive: R is transitive if, whenever (a, b) and (b, c) are both in R, (a, c) is also in R.
The only pair in R is (1, 2). A chain would need a pair starting with 2, and there is none.
So there is no case that breaks the rule, and R is transitive.
Why the other options are incorrect
Option (2) symmetric but not transitive — Incorrect. (2, 1) is missing, so R is not symmetric, and R is transitive.
Option (3) reflexive but not transitive — Incorrect. (1, 1) is missing, so R is not reflexive, and R is transitive.
Option (4) neither reflexive, nor symmetric, nor transitive — Incorrect. R is transitive, because no two of its pairs form a chain.