On A={1,2,3,4}, let R={(1,2),(2,4),(1,4),(3,3)}. Is R transitive?
Answer and explanation
Correct answer: Yes
Use the rule: whenever (a,b) and (b,c) belong to R, (a,c) must also belong to R. The only nontrivial chain is (1,2) followed by (2,4), and its required result (1,4) is already present. The pair (3,3) leads only to itself, which is present. No reverse pair such as (2,1) or (4,1) is demanded, so R is transitive and option A is correct.
Frequently asked questions
What is the correct answer to this question?
Yes
Why is this the correct answer?
Use the rule: whenever (a,b) and (b,c) belong to R, (a,c) must also belong to R. The only nontrivial chain is (1,2) followed by (2,4), and its required result (1,4) is already present. The pair (3,3) leads only to itself, which is present. No reverse pair such as (2,1) or (4,1) is demanded, so R is transitive and option A is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Transitive relation.
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