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  • 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

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.

Answers (1)

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

(i) Assume, f: A \rightarrow B \text{ denote a mapping}

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

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

(ii) Again assume, g: A \rightarrow B  denotes a mapping: g = \{ (2, 2), (3, 2), (4, 5) \}   . Hence, it is not an injective mapping.

(iii) Again assume, h: B \rightarrow A denotes a mapping: h = \{ (2, 2), (5, 3), (6, 4), (7, 4) \}   . Hence, it is a mapping from B to A.

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infoexpert22

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