Chapter 1.1, Problem 10.4E

Let $ℝ$ denote the set of real numbers. For each of the following subsets of $ℝ\times ℝ$, determine whether it is equal to the cartesian product of two subsets of $ℝ$.

$\left\{\left(x,y\right)|x\text{is}\text{not}\text{an}\text{integer}\text{and y is an integer}\right\}.$