Question

Let A be the set of all students of a boys school. Show that the relation Rin 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​

Answer 1

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Solution Since the school is boys school, no student of the school can be sister of anystudent of the school. Hence, R = φ, showing that R is the empty relation. It is alsoobvious that the difference between heights of any two students of the school has to beless than 3 meters. This shows that R′ = A × A is the universal relation.