On A={1,2,3}, what is the smallest addition to R={(1,2),(2,3)} that makes R transitive?
Answer and explanation
Correct answer: (1,3)
Transitivity requires that whenever (a,b) and (b,c) are in the relation, (a,c) must also be present. Here (1,2) and (2,3) are present, so the required consequent pair is (1,3). Adding it creates no further two-step chain that demands another missing pair. The other proposed pairs do not satisfy this specific requirement.
Frequently asked questions
What is the correct answer to this question?
(1,3)
Why is this the correct answer?
Transitivity requires that whenever (a,b) and (b,c) are in the relation, (a,c) must also be present. Here (1,2) and (2,3) are present, so the required consequent pair is (1,3). Adding it creates no further two-step chain that demands another missing pair. The other proposed pairs do not satisfy this specific requirement.
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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