I hope this doesn't belong in the pre-algebra section.

Sorry for so many questions

1. X is the set of elements x, where x is a natural number, and Y = {0,1}. Given that f, the mapping from X to Y, is the remainder when x is divided by 2, determine the following values.

[sol]

f(1)=1

f(2)=0

f(3)=1

f(4)=0

f(5)=1

Can someone explain what this question is asking? I have no idea what this question is asking, like what is "Given that f, the mapping from X to Y, is the remainder when x is divided by 2"???

I also don't get this

2. is --- (1)

In (1), the images of the elements in X differ. (Why? What do they mean by differ anyway?)

How do you know if a function is a one to one mapping? I'm asking how do you figure it out if the two functions share two or more points where they share the same value (parabolas are obvious, but how about cubic functions?)

3. Given that f(n) is the amount of numbers from 1 to n which are relatively prime to n, complete the following exercises.

a) Determine f(2), f(3), f(4), f(5), f(6), and f(7).

I have no idea what the question is asking me. No idea on even how to start.

b) Given that the domain of f(n) is { }, determine the range.