Prove that in $A$ with $m(A)>0$, $\exists x,y\in A$ s.t. $x\neq y$ and $x-y\in\mathbb{Q}$

Question

I need help with this proof:

" Let $A\subseteq\mathbb{R}$ be a measurable set with $m(A)>0$. Prove that $\exists x,y\in A$ which verify that $x\neq y$ and $x-y\in\mathbb{Q}$"

At first i think about using that, given any two real numbers $a,b\in\mathbb{R}$ ($a<b$), then $\exists q \in\mathbb{Q}$ so that $a<q<b$, but i'm sure if it's the right way.