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
The Correct Option is D
Solution and 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 that, Range (R) = {b: (a, b) ∈ R}Therefore, range (R) = {1, 2, 3, 4, 6} = A⇒ n(A) = 5Hence, the correct option is (D).
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