If R = {(1,2), (2,3)}, why is R not transitive?
Answer and explanation
Correct answer: (1,3) अनुपस्थित है
The definition of transitivity says that if (a,b) ∈ R and (b,c) ∈ R, then (a,c) must also be in R. Since (1,2) and (2,3) are both in R, the required consequence is (1,3). That pair is absent, so the relation fails the condition and is not transitive. Reverse pairs and diagonal pairs are not required for this specific test; therefore A is correct.
Frequently asked questions
What is the correct answer to this question?
(1,3) अनुपस्थित है
Why is this the correct answer?
The definition of transitivity says that if (a,b) ∈ R and (b,c) ∈ R, then (a,c) must also be in R. Since (1,2) and (2,3) are both in R, the required consequence is (1,3). That pair is absent, so the relation fails the condition and is not transitive. Reverse pairs and diagonal pairs are not required for this specific test; therefore A is correct.
Which subject and chapter does this question cover?
This is a Class 11 Mathematics question. Chapter: Relations and Functions. Topic: Relations.
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