Which pair of transitive relations gives a union that is not transitive?
Answer and explanation
Correct answer: R={(1,2)}, S={(2,3)}
Every singleton relation containing only (1,2) or only (2,3) is transitive, because there is no pair of consecutive arrows within that relation requiring an additional pair. Their union contains (1,2) and (2,3), but not (1,3), so transitivity fails. The other choices produce relations whose unions remain transitive, such as an identity, empty, or universal relation.
Frequently asked questions
What is the correct answer to this question?
R={(1,2)}, S={(2,3)}
Why is this the correct answer?
Every singleton relation containing only (1,2) or only (2,3) is transitive, because there is no pair of consecutive arrows within that relation requiring an additional pair. Their union contains (1,2) and (2,3), but not (1,3), so transitivity fails. The other choices produce relations whose unions remain transitive, such as an identity, empty, or universal relation.
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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