If R = {(1, 2), (2, 4), (1, 4)}, which pair is required in the transitive check?
Answer and explanation
Correct answer: (1, 4)
The governing concept is transitivity. A relation is transitive if (a,b) and (b,c) in R require (a,c) to be in R as well. Here the first two given pairs form a chain: (1,2) and (2,4). Matching the second component of the first pair with the first component of the second gives a required conclusion of (1,4). That pair is present in R, so the displayed chain passes the transitive check. Therefore option B is correct. Pair (4,1) would concern a reverse direction not supplied by the chain; (2,1) is not the required outer pair; and (4,4) does not follow from the two given pairs. The calculation is about connecting the first element to the final element.
Frequently asked questions
What is the correct answer to this question?
(1, 4)
Why is this the correct answer?
The governing concept is transitivity. A relation is transitive if (a,b) and (b,c) in R require (a,c) to be in R as well. Here the first two given pairs form a chain: (1,2) and (2,4). Matching the second component of the first pair with the first component of the second gives a required conclusion of (1,4). That pair is present in R, so the displayed chain passes the transitive check. Therefore option B is correct. Pair (4,1) would concern a reverse direction not supplied by the chain; (2,1) is not the required outer pair; and (4,4) does not follow from the two given pairs. The calculation is about connecting the first element to the final element.
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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