Let A = {1, 2, 3} and R = {(a, b) : a divides b}. Is R reflexive on A?
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Answer and explanation
Correct answer: Yes
A relation on A is reflexive when (a, a) belongs to R for every a in A. Here, 1 divides 1, 2 divides 2 and 3 divides 3, because every non-zero integer divides itself. Thus (1,1), (2,2) and (3,3) are all in R, so option A is correct. Options C and D check only part of the required condition.
Frequently asked questions
What is the correct answer to this question?
Yes
Why is this the correct answer?
A relation on A is reflexive when (a, a) belongs to R for every a in A. Here, 1 divides 1, 2 divides 2 and 3 divides 3, because every non-zero integer divides itself. Thus (1,1), (2,2) and (3,3) are all in R, so option A is correct. Options C and D check only part of the required condition.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
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