Which of the following sets are dense in $\mathbb R^2$ with respect to the usual topology.
$\{ (x, y)\in\mathbb R^2 : x\in\mathbb N\}$
$\{ (x, y)\in\mathbb R^2 : x+y\in\mathbb Q\}$
$\{ (x, y)\in\mathbb R^2 : x^2 + y^2 = 5\}$
$\{ (x, y)\in\mathbb R^2 : xy\neq 0\}$.
Any hint is welcome.