Let

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

Determine whether A is open, closed or neither. What is the closure, interior and boundary of A?

I was under the impression that the set is neither open nor closed, but am struggling to prove this.