If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in range of R ?

Concept:

Range of a Relation: Let R be a relation from set A to set B. Then, the set of all second components of the ordered pair belonging to relation R forms the range of the relation R.

i.e Range (R) = {b: (a, b) ∈ R}.

Calculation:

Given: A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a}

The given R can be re-written in roaster form as R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}.

As we know that, Range (R) = {b: (a, b) ∈ R}.

⇒ Range (R) = {1, 2, 3, 4, 6} = A

⇒ n(A) = 5

Hence, option 4 is the correct answer.