On A={1,2,3}, let R={(1,2),(2,3)}. Why is R not transitive?
Answer and explanation
Correct answer: Because (1,3) is missing
A relation R is transitive when, for any a, b, and c, the presence of (a,b) and (b,c) guarantees the presence of (a,c). Here, (1,2) and (2,3) are both in R, so transitivity requires (1,3). That ordered pair is absent. The reverse pair (2,1) and self-pair (1,1) are not required by transitivity, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
Because (1,3) is missing
Why is this the correct answer?
A relation R is transitive when, for any a, b, and c, the presence of (a,b) and (b,c) guarantees the presence of (a,c). Here, (1,2) and (2,3) are both in R, so transitivity requires (1,3). That ordered pair is absent. The reverse pair (2,1) and self-pair (1,1) are not required by transitivity, so 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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