0 votes 0 votes 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) $n^{2}$ Set Theory & Algebra iiith-pgee functions + – Tesla! asked Apr 21, 2018 Tesla! 1.1k views answer comment Share Follow See 1 comment See all 1 1 comment reply Registered user 48 commented Apr 21, 2018 reply Follow Share 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 0 votes 0 votes Please log in or register to add a comment.
1 votes 1 votes 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. abhishekmehta4u answered Apr 21, 2018 abhishekmehta4u comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments tusharp commented Mar 31, 2019 reply Follow Share @abhishekmehta4u sir isn't it a contradiction :( . They just gave the domain in the question (Natural numbers). Functions are as defined below. 0 votes 0 votes tusharp commented Mar 31, 2019 reply Follow Share @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. 1 votes 1 votes Tejas k commented Jun 22, 2020 reply Follow Share DOUBT!! in option a , for last element on co-domain won't be having any pre-image , then how a option is onto 0 votes 0 votes Please log in or register to add a comment.