On A = {1, 2, 3}, R = {(1,2), (2,3), (1,3)} is given. Is R transitive?
Answer and explanation
Correct answer: Yes, because the required pair (1,3) is present
Transitivity requires that whenever (a,b) and (b,c) belong to R, the pair (a,c) must also belong to R. In this relation, the only nontrivial chain is (1,2) followed by (2,3), which requires (1,3). That required pair is explicitly present. Other possible chains do not create a missing requirement: there are no pairs beginning with 3, and the available links do not produce another unfulfilled chain. Therefore R is transitive, so option A is correct. Reverse pairs are relevant to symmetry, not transitivity.
Frequently asked questions
What is the correct answer to this question?
Yes, because the required pair (1,3) is present
Why is this the correct answer?
Transitivity requires that whenever (a,b) and (b,c) belong to R, the pair (a,c) must also belong to R. In this relation, the only nontrivial chain is (1,2) followed by (2,3), which requires (1,3). That required pair is explicitly present. Other possible chains do not create a missing requirement: there are no pairs beginning with 3, and the available links do not produce another unfulfilled chain. Therefore R is transitive, so option A is correct. Reverse pairs are relevant to symmetry, not transitivity.
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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