GO Classes Test Series 2024 | Discrete Mathematics | Test 2 | Question: 13

GO Classes asked Apr 21, 2022 • retagged Apr 27, 2023 by Lakshman Bhaiya

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The below function is defined from a set of all positive integers to a set of all integers.

$f(n) = \left\{\begin{matrix} (n-1)/2\;;& \text{if}\; n \;\text{is odd} \\ -n/2\;;& \text{if}\; n\;\text{is even} \end{matrix}\right.$

Which of the following statements is true?

It is one to one but not onto
It is onto but not one-one
It is bijection
It is neither One-One nor Onto

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GO Classes asked Apr 21, 2022 • retagged Apr 27, 2023 by Lakshman Bhaiya

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mayank pathak

commented Jul 20, 2022

in this question 0 is not consider in positive integer must be mention because 0 can change their ans

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shadymademe

commented Jul 20, 2022

0 is neither positive nor negative.

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$f(n)$ is : $Z^+\rightarrow Z$
$0$ is neither positive nor negative. Hence, $0 \notin Z^+$

$f(1) = 0; \hspace{0.5cm} f(3) = 1;\hspace{0.5cm} f(5) = 2;$ and so on…
$f(2) = -1;\hspace{0.5cm} f(4) = -2;\hspace{0.5cm} f(6) = -3;$ and so on…

We can see, $f(n)$ is One to One and Onto $\implies$ bijection.

sidd_07 answered May 30, 2022 • selected Jul 20, 2022 by Deepak Poonia

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