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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    On the set of integers Z, define \[f:z\to z\] as \[f(n)=\left\{ \begin{matrix}    \frac{n}{2}, & n\,is\,\,even  \\    0, & n\,\,\,is\,\,odd  \\ \end{matrix} \right.\], then f is

    A)  injective but not subjective

    B)  neither injective nor subjective

    C)  surjective but not injective

    D)  objective

    Correct Answer: C

    Solution :

    Given,  \[f(n)=\left\{ \begin{matrix}    \frac{n}{2}, & n\,\,is\,even  \\    0, & n\,is\,odd  \\ \end{matrix} \right.\] Here, we see that for every odd values of z, it will give zero. It means that it is a many one function. For every even values of z, we will get a set of integers \[(-\infty ,\infty )\]. So, it is onto. Hence, it is subjective but not injective.


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