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# Which of the Following Functions From A To B Are One-one and Onto? F1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7} - CBSE (Commerce) Class 12 - Mathematics

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#### Question

Which of the following functions from A to B are one-one and onto?
f1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}

#### Solution

f1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7}

njectivity:
f1 (1) = 3
f1 (2) = 5
f1 (3) = 7

⇒ Every element of has different images in B.
So, f1 is one-one.

Surjectivity:
Co-domain of f1 = {3, 5, 7}
Range of f1 =set of images  =  {3, 5, 7}

⇒ Co-domain = range
So, f1 is onto.

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Solution Which of the Following Functions From A To B Are One-one and Onto? F1 = {(1, 3), (2, 5), (3, 7)} ; A = {1, 2, 3}, B = {3, 5, 7} Concept: Types of Functions.
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