Let A be the set of all students of a girls’ school, and let R be the relation on A given by \(R = \{(a, b) : a \text{ is a brother of } b\}\). Then R is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → the empty relation
Every student of the school is a girl, so no student a can be a brother of any student b.
So no ordered pair (a, b) of students belongs to R, and \(R = \phi\), the empty relation.
It is not reflexive, since \((a, a) \notin R\) for any student a. So it is not an equivalence relation either, and it is not the universal relation \(A \times A\).