On A={1,2,3}, let R={(1,2),(2,2),(2,3),(1,3)}. Is R transitive?
Answer and explanation
Correct answer: Yes
Check every composable pair. From (1,2) and (2,2), the required pair is (1,2), already present. From (2,2) and (2,3), the required pair is (2,3), also present. From (1,2) and (2,3), the required pair is (1,3), present as well. There are no pairs beginning with 3, so no further condition arises. Therefore 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?
Check every composable pair. From (1,2) and (2,2), the required pair is (1,2), already present. From (2,2) and (2,3), the required pair is (2,3), also present. From (1,2) and (2,3), the required pair is (1,3), present as well. There are no pairs beginning with 3, so no further condition arises. Therefore 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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