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.

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Example 1: 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. 


Ans: Since, the school is boys school, no student of the school can be sister of any student of the school. Hence, R = ∅,  showing that R is the empty relation. It is also obvious that the difference between heights of any two students of the school has to less than 3 metres. This shows that R' = A X A is the universal relation.

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