1 votes 1 votes I think only d) is correct Set Theory & Algebra set-theory&algebra functions discrete-mathematics zeal zeal2019 + – Prince Sindhiya asked Dec 22, 2018 • edited Mar 6, 2019 by ajaysoni1924 Prince Sindhiya 815 views answer comment Share Follow See all 4 Comments See all 4 4 Comments reply BharathiCH commented Dec 22, 2018 reply Follow Share Real numbers can't be in one-to-one correspondence since it is uncountable. For natural numbers and integers the co-domain is not equal to range. Rational numbers will hold true for the function here.. 0 votes 0 votes Shaik Masthan commented Dec 22, 2018 reply Follow Share @Prince Sindhiya again posting screenshot unnecessarily. If you do this, we can't find duplicates, hence more redundancy in GO platform and Moreover our time will be wasted unnecessarily. I know to type it takes 10-15 min, but atleast for next time if someone ask the same question i can easily find this search 1 votes 1 votes Shobhit Joshi commented Dec 22, 2018 reply Follow Share @Prince Sindhiya 4 would be correct, 1 and 2 cannot but why not 3 ? 0 votes 0 votes aryavart commented Jul 8, 2021 i edited by aryavart Jul 8, 2021 reply Follow Share f(12(x−1))=2(12(x−1))+1=(x−1)+1=x, therefore surjective. Now suppose f(x1)=f(x2) then f(x1)2x1+12x1x1=f(x2)=2x2+1=2x2=x2, therefore injective. Ref: https://math.stackexchange.com/a/1696547/864381 I think this reasoning is applied for Rational numbers too. Therefor answer is (C). 0 votes 0 votes Please log in or register to add a comment.