Question

If A = {2, 3, 4} and B = {3, 4, 5, 6, 7, 8} : A relation if from A to B is defined such that “x divides y” then R^-1 is

(A) {(4, 2), (6, 2), (8, 2), (3, 3), (6,3), (4, 4), (8, 4)}

(B) {(2, 4), (2, 6), (2, 8), (3, 3), (3, 6), (4, 4), (4, 8)}

(C) {(3, 3), (4, 4), (8, 4)}

(D) {(4, 2), (6, 3), (8, 4)}

Answer 1

Answer is (A)

Given sets are

A = {2, 3, 4} and B = {3, 4, 5, 6, 7, 8}

Relation R from A to B is defined as

“x divides y” ∀ x ∈ A, y ∈ B

So, when x = 2 ∈ A

Then 2 divides the element 4, 6, 8 of B.

So, (2, 4), (2, 6), (2, 8) ∈ R

when x = 3 ∈ A, then 3 divides elements 3, 6 of B

So, (3, 3), (3, 6) ∈ R

when x = 4 ∈ A then 4 divides the elements 4, 8 of B.

So, (4, 4), (4, 8) ∈ R

R = {(2, 4), (2, 6), (2, 8), (3, 3), (3, 6), (4, 4), (4, 8)}

R^-1 = {(4, 2), (6, 2), (8, 2), (3, 3), (6, 3), (4, 4), (8, 4)}