Trying to find the right answer to this..

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’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.

Since the school is boys school i.e. there is not girl student no student of the school can be sister of any student of the school.
∴ R ⇒ R is the empty relation.
Clearly the difference between heights of a and b is less than 3 metres.
∴ R’ = A x A is the universal relation.

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Relations and Functions

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’ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation.