If R={(1,1),(1,2),(2,2)}, which pair is required from (1,2) and (2,2) in a transitive check?
Answer and explanation
Correct answer: (1,2)
For transitivity, use the pattern (a,b) and (b,c), then require (a,c). Here the first given pair is (1,2), so a=1 and b=2. The second pair is (2,2), so b=2 and c=2. Matching the common middle component is the key step. Therefore the required conclusion is (a,c)=(1,2), which is option A. That pair is already present in R, so this particular chain satisfies the transitive requirement. Option B reverses the ordered pair, while options C and D do not use the first and last components of the chain in the required way. This checks one implication; a complete proof would inspect every applicable chain.
Frequently asked questions
What is the correct answer to this question?
(1,2)
Why is this the correct answer?
For transitivity, use the pattern (a,b) and (b,c), then require (a,c). Here the first given pair is (1,2), so a=1 and b=2. The second pair is (2,2), so b=2 and c=2. Matching the common middle component is the key step. Therefore the required conclusion is (a,c)=(1,2), which is option A. That pair is already present in R, so this particular chain satisfies the transitive requirement. Option B reverses the ordered pair, while options C and D do not use the first and last components of the chain in the required way. This checks one implication; a complete proof would inspect every applicable chain.
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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