If R and S are transitive relations on the same set, which statement about their union R∪S is always valid?
Answer and explanation
Correct answer: R∪S need not be transitive
The union of two transitive relations is not guaranteed to be transitive because a first pair may come from R and a second pair from S, while the required composite pair belongs to neither relation. For example, R={(1,2)} and S={(2,3)} are both transitive, but R∪S lacks (1,3). Hence option B is the only always valid statement.
Frequently asked questions
What is the correct answer to this question?
R∪S need not be transitive
Why is this the correct answer?
The union of two transitive relations is not guaranteed to be transitive because a first pair may come from R and a second pair from S, while the required composite pair belongs to neither relation. For example, R={(1,2)} and S={(2,3)} are both transitive, but R∪S lacks (1,3). Hence option B is the only always valid statement.
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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