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

[SD83]

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.

 

[pka]

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.

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.View attachment 15161

Question: Is it not the case that \(\displaystyle 2\in f^{-1}(S)~~?\) SEE HERE