Question

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 the range of R?

• A. 2
• B. 4
• C. 6
• D. 5

Answer 1

Answer: (D)

5

Answer 2

Explanation:
It is given that 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, Range (R) = {b: (a, b) ∈ R}
Therefore, range (R) = {1, 2, 3, 4, 6} = A∈ n(A) = 5
Hence, the correct option is (D).