PGEE 2018

Question

Consider function f: N $\rightarrow$ N, where N is a natural number, which of the following function is not one to one but onto

A) f(1)=f(2)=1 f(n)=n-1

B) 2n

C) $n^{2}$

Comments

Does natural number includes zero?
This is bit ambiguous, it's not mentioned, whether natural number includes zero or not.

if it includes zero,  then f(0)= -1 which is out of the domain.

https://www.intmath.com/blog/mathematics/is-0-a-natural-number-365

Answer 1

option a 

f(1) and f(2) both are mapped to 1 so it is not one to one. and there is no blank in co-domain so it is onto.

Comments

@abhishekmehta4u sir isn't it a contradiction :( . They just gave the domain in the question (Natural numbers). Functions are as defined below.

---

@Verma Ashish @abhishekmehta4u sorry my bad I missed it. To avoid it, they have already given f(1) and f(2).

Thanks for the help.

---

DOUBT!!

in option a , for last element on co-domain won't be having any pre-image ,

then how a option is onto