Consider the following statements : 1. A function f: Z Z , defined by f(x)=x+1, is one-one as well as onto. 2. A function f: N N , defined by f(x)=x+1, is one-one but not onto. Which of the above statements is/are correct?

NDA 2021 Mathematics question

Consider the following statements : 1. A function , defined by , is one-one as well as onto. 2. A function , defined by , is one-one but not onto. Which of the above statements is/are correct?

(A)1 only
(B)2 only
(C)Both 1 and 2Correct
(D)Neither 1 nor 2

Answer: (C)

Solution

In both cases , so is one-one. Statement 1: For any integer , is also an integer and , so every integer has a pre-image; is

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Question ID VK-033529