Which relation on A={1,2,3} is transitive but not symmetric?
Answer and explanation
Correct answer: R={(1,1),(2,2),(1,2)}
For option A, the only nontrivial chain is (1,2) followed by (2,2), which requires (1,2), already present; chains involving diagonal pairs also remain inside the relation. Thus it is transitive. It is not symmetric because (1,2) is present while (2,1) is absent. Option B is symmetric, option C fails symmetry and transitivity checks involving reverse directions, and option D is not transitive because (1,2) and (2,3) occur without (1,3).
Frequently asked questions
What is the correct answer to this question?
R={(1,1),(2,2),(1,2)}
Why is this the correct answer?
For option A, the only nontrivial chain is (1,2) followed by (2,2), which requires (1,2), already present; chains involving diagonal pairs also remain inside the relation. Thus it is transitive. It is not symmetric because (1,2) is present while (2,1) is absent. Option B is symmetric, option C fails symmetry and transitivity checks involving reverse directions, and option D is not transitive because (1,2) and (2,3) occur without (1,3).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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