Which relation on A={1,2,3} is transitive but not reflexive?
Answer and explanation
Correct answer: R={(1,1),(2,2),(1,2),(2,1)}
Option B is correct. The only composable pair in B is (1,2) followed by (2,3), and the required pair (1,3) is missing, so B is not transitive; therefore this option cannot be correct. Option A is transitive but also reflexive. Option C is transitive on {1,2} but fails reflexivity on A because (3,3) is absent. Option D is not transitive because (2,1) and (1,2) would require (2,2). Hence option C is the required relation.
Frequently asked questions
What is the correct answer to this question?
R={(1,1),(2,2),(1,2),(2,1)}
Why is this the correct answer?
Option B is correct. The only composable pair in B is (1,2) followed by (2,3), and the required pair (1,3) is missing, so B is not transitive; therefore this option cannot be correct. Option A is transitive but also reflexive. Option C is transitive on {1,2} but fails reflexivity on A because (3,3) is absent. Option D is not transitive because (2,1) and (1,2) would require (2,2). Hence option C is the required relation.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Transitive relation.
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