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 is sister of b} is the empty relation and `R^(prime)`= {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Explanation

To solve the problem, we need to show two things:

1. The relation \( R = \{(a, b) : a \text{ is the sister of } b\} \) is the empty relation.
2. The relation \( R' = \{(a, b) : \text{the difference between heights of } a \text{ and } b \text{ is less than 3 meters}\} \) is the universal relation.

### Step 1: Show that \( R \) is the empty relation

- **Definition of the set \( A \)**: Let \( A \) be the set of all students of a boys' school. This means that every element \( a \) in \( A \) is a boy.
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