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Which of the Following Functions From A To B Are One-one and Onto? F2 = {(2, A), (3, B), (4, C)} ; A = {2, 3, 4}, B = {A, B, C} - CBSE (Science) Class 12 - Mathematics

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Question

Which of the following functions from A to B are one-one and onto?

 f2 = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {abc}

Solution

f2 = {(2, a), (3, b), (4, c)} ; A = {2, 3, 4}, B = {abc}

Injectivity:
f2 (2) = a
f2 (3) = b
f2 (4) = c

⇒ Every element of A has different images in B.
So, f2 is one-one.

Surjectivity:
Co-domain of f2 = {abc}

Range of f2 = set of images = {abc}

⇒ Co-domain = range

So, f2 is onto.

 

  Is there an error in this question or solution?
Solution Which of the Following Functions From A To B Are One-one and Onto? F2 = {(2, A), (3, B), (4, C)} ; A = {2, 3, 4}, B = {A, B, C} Concept: Types of Functions.
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