Closed sets of $Spec(R)$.

Question

I have to dounbs: Let $R$ be the ring $\mathbb{C}[x]_{(x)}$. So we have that $Spec(R)=\{(0),(x)\}$. I have to descrive closed sets of $Spec(R)$. I think that they are $\{\emptyset, Spec(R), (x) \}$ and $(0)$ is not open or closed. Is it correct? If we consider $R=\mathbb{C}[x,y,z,w]/I$ where $I=(wz-xy,wy-x^2,xz-y^2)$ how can I find closed sets of $Spec(R)$?