On A = {1, 2, 3}, let R = {(a, b) : a² = b²}. Is R reflexive?
Answer and explanation
Correct answer: Yes
To test reflexivity, we must check whether (a, a) belongs to R for every a in A. Substituting b = a into the defining condition gives a² = a², which is an identity and is true for a = 1, 2, and 3. Therefore (1, 1), (2, 2), and (3, 3) all belong to R. The relation may contain additional pairs as well, but those are irrelevant to reflexivity. Hence R is reflexive and option A is correct; options C and D wrongly limit the condition to selected elements.
Frequently asked questions
What is the correct answer to this question?
Yes
Why is this the correct answer?
To test reflexivity, we must check whether (a, a) belongs to R for every a in A. Substituting b = a into the defining condition gives a² = a², which is an identity and is true for a = 1, 2, and 3. Therefore (1, 1), (2, 2), and (3, 3) all belong to R. The relation may contain additional pairs as well, but those are irrelevant to reflexivity. Hence R is reflexive and option A is correct; options C and D wrongly limit the condition to selected elements.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
