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Let A be the set of all students of a b...

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.

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To solve the problem, we need to analyze two relations defined on the set of all students of a boys' school, denoted as set A. ### Step 1: Analyze the Relation R The relation R is defined as: \[ R = \{(a, b) : a \text{ is sister of } b\} \] Since A is the set of all students in a boys' school, there are no girls in this set. Therefore, it is impossible for any student (a boy) to have a sister (as sisters are female). ...
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