Find the set of Pre-Images from F:N>{0,1,2} where F(x) = 3 m

[Guest]

Hi, I am studying discrete maths and i have a practise question that I'm not sure which way to answer correctly. I need to find the set of pre-images of a function F:N>{0,1,2} where F(x) = 3 mod 3, where F(x) is the remainder when x is divided by 3. Please see image of my question and answer attached. I have attached the screenshot of the question and my answer. If anyone can help that would be appreciated.

[HallsofIvy]

You mean F(x)= x (mod 3). not "F(x)= 3 (mod 3)".

F of any multiple of 3 is 0 so the preimage. [tex]F^{-1}(\{0\})= \{x| x= 3k\}[/tex] for k any integer. Similarly if x= 3k+ 1 then F(x)= 1 and if x= 3k+ 2, F(x)= 2 so [tex]F^{-1}(\{1\})= \{x| x= 3k+1\}[/tex] anx [tex]F^{-1}(\{2\})= \{x| x= 3k+ 2\}[/tex].