I came across a question which goes as follows:-
Let $S$ be a set defined as follows:- $S=\{(x,y)|(x,y)\in \mathbb{R}{\times} \mathbb{R} $ where $x\notin \mathbb{Z}$ and $y\notin \mathbb{Q}\}.$ Now, my question goes as follows:-
Can $S$ be also written as $\mathbb{R} \setminus \mathbb{Z}\times \mathbb{R} \setminus \mathbb{Q}$ ?