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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}

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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}

Sum
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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.

 

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Chapter 2: Functions - Exercise 2.1 [Page 31]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 2 Functions
Exercise 2.1 | Q 2.2 | Page 31

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