Let $A$ be the set of all students of a boys' school. Show that the relation $R$ in $A$ given by $R = \{(a, b) : a \text{ is sister of } b\}$ is the empty relation and $R^{\prime} = \{(a, b) : \text{the difference between heights of } a \text{ and } b \text{ is less than } 3 \text{ meters}\}$ is the universal relation.

(N/A) Since the school is a boys' school,no student of the school can be a sister of any other student of the school.
Therefore,$R = \phi$,which shows that $R$ is the empty relation.
It is also obvious that the difference between the heights of any two students of the school must be less than $3 \text{ meters}$ (as the maximum height of a human is typically less than $3 \text{ meters}$).
This shows that $R^{\prime} = A \times A$,which is the universal relation.