Prove that $A$ is connected Q. Prove that: If we remove 12 points from the Euclidean plane $\mathbb{R}^2$ to get set $A$, then $A$ is connected.
I don't really understand how to proceed with the question. I thought of going via contradiction but I am stuck. Should I approach it via path connectedness?

If you remove the whole $\mathbb{Q}^2$ (i.e. the set $\mathbb{R}^2 - \mathbb{Q}^2$), you still get a path connected set. You can find the proof of this on this website.
