1. ## Product Sets Help

Hi everyone,

I was wondering if someone felt inclined to give me a hand understanding a question that I'm stuck on? It's really bugging me because I think I'm missing something quite simple here!

The question is:

For each of the following subsets of $\displaystyle \mathbb{R} \times \mathbb{R}$, determine whether it can be written as a product of two subsets of $\displaystyle \mathbb{R}$. If it can, what are these subsets?

(i) $\displaystyle A_{1} = {(x,y) : 0 \leq y < 1}$
(ii) $\displaystyle A_{2} = {(x,y) : x^2 + y^2 < 3}$
(iii) $\displaystyle A_{3} = {(x,y) : x<y}$
(iv) $\displaystyle A_{4} = {(x,y) : x \mbox{ is an integer, and }y \mbox{ is not an integer}}$

As I said, I'm sure I'm missing something fairly simple but I'm really not sure what it is!

(i) $\displaystyle A_{1} = {(x,y) : 0 \leq y < 1} = \mathbb{R} \times [0,1[$