Which relation on A={1,2,3} is symmetric but not transitive?
Answer and explanation
Correct answer: R={(1,2),(2,1),(1,3),(3,1)}
In option A, every ordered pair has its reverse, so the relation is symmetric. However, (2,1) and (1,3) belong to R, while (2,3) does not; hence transitivity fails. Option B is the identity relation and is transitive, option C is transitive for the displayed chain, and the universal relation in option D is both symmetric and transitive. Therefore only option A has the required two properties.
Frequently asked questions
What is the correct answer to this question?
R={(1,2),(2,1),(1,3),(3,1)}
Why is this the correct answer?
In option A, every ordered pair has its reverse, so the relation is symmetric. However, (2,1) and (1,3) belong to R, while (2,3) does not; hence transitivity fails. Option B is the identity relation and is transitive, option C is transitive for the displayed chain, and the universal relation in option D is both symmetric and transitive. Therefore only option A has the required two properties.
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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