Which statement about two transitive relations R and S on the same set is not necessarily true?
Answer and explanation
Correct answer: R∪S is transitive
Option B is correct because the union of two transitive relations need not be transitive. For example, let R={(1,2)} and S={(2,3)}; each relation is transitive because it has no composable pair, but R∪S contains (1,2) and (2,3) without containing (1,3). The intersection is always transitive: any pair present in it belongs to both relations, so transitivity in both supplies the composite pair. Options C and D are also true.
Frequently asked questions
What is the correct answer to this question?
R∪S is transitive
Why is this the correct answer?
Option B is correct because the union of two transitive relations need not be transitive. For example, let R={(1,2)} and S={(2,3)}; each relation is transitive because it has no composable pair, but R∪S contains (1,2) and (2,3) without containing (1,3). The intersection is always transitive: any pair present in it belongs to both relations, so transitivity in both supplies the composite pair. Options C and D are also true.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Transitive relation.
