Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of

1.	Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:(a) an injective mapping from A to B(b) a mapping from A to B which is not injective(c) a mapping from B to A.
Answer» Given, A = {2, 3, 4}, B = {2, 5, 6, 7} (i) Let f: A → B denote a mapping f = {(x, y): y = x + 3} or f = {(2, 5), (3, 6), (4, 7)}, which is an injective mapping. (ii) Let g: A → B denote a mapping such that g = {(2, 2), (3, 2), (4, 5)}, which is not an injective mapping. (iii) Let h: B → A denote a mapping such that h = {(2, 2), (5, 3), (6, 4), (7, 4)}, which is one of the mapping from B to A.

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of each of the following:(a) an injective mapping from A to B(b) a mapping from A to B which is not injective(c) a mapping from B to A.

Answer»

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

(i) Let f: A → B denote a mapping

f = {(x, y): y = x + 3} or

f = {(2, 5), (3, 6), (4, 7)}, which is an injective mapping.

(ii) Let g: A → B denote a mapping such that g = {(2, 2), (3, 2), (4, 5)}, which is not an injective mapping.

(iii) Let h: B → A denote a mapping such that h = {(2, 2), (5, 3), (6, 4), (7, 4)}, which is one of the mapping from B to A.