Question

If A = {1, 2, 3), B = {4, 5, 6) which of following are relations from A to B.
i) R₁ = {(1, 4), (1, 5), (1, 6)}
ii) R₂ = {(1, 5), (2, 4), (3. 6)}
iii) R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}
iv) R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)}

Answer 1

it is given that, A = {1, 2, 3} and B = {4, 5, 6}

we have to get relation from A to B.

concept : every element of set A is associated with unique element of set B.
No element of A must have more than one image.

now let's check all options,

(i) here, f(1) = 4 and f(1) = 5 it's not possible.
so, this relation is not mapping from A to B.

(ii) here, f(1) = 5, f(2) = 4 and f(3) = 6 every element of set A is associated with unique element of set B. hence, it is relation from A to B.

(iii) this is same condition as (i) . it's not relation from A to B.

(iv) no, it's not relation because we have to write relation from A to B. but here also elements of B used in place of A.