On A = {1, 2, 3}, R = {(1,2), (2,3)}. Why is R not transitive?
Answer and explanation
Correct answer: Because (1,3) is absent
The governing rule for transitivity is: if (a,b) ∈ R and (b,c) ∈ R, then (a,c) must be in R. Here, (1,2) and (2,3) are both present, so transitivity requires (1,3). However, (1,3) is not listed in R. This single missing consequence is enough to disprove transitivity. The absence of (1,1), (3,2), or (2,1) is irrelevant because those pairs are not required by the displayed linked chain. Therefore option A correctly identifies the failure.
Frequently asked questions
What is the correct answer to this question?
Because (1,3) is absent
Why is this the correct answer?
The governing rule for transitivity is: if (a,b) ∈ R and (b,c) ∈ R, then (a,c) must be in R. Here, (1,2) and (2,3) are both present, so transitivity requires (1,3). However, (1,3) is not listed in R. This single missing consequence is enough to disprove transitivity. The absence of (1,1), (3,2), or (2,1) is irrelevant because those pairs are not required by the displayed linked chain. Therefore option A correctly identifies the failure.
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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