How do I prove that the set

$\displaystyle A=\left\{ \left(a,b\right)=\in\mathbb{R}^{2}:\:0\leq x<3,\:0\leq y\leq5\right\}$

is open, closed or neither? I believe it to be neither, because of the x<3 condition.

What would the closure, interior and boundary of the set A be?

Thanks in advance.