Convexity Proof for $\mathbb R ^n \backslash A$

Question

I need to tell if it is true or false and prove that given $A$ a convex set, $\mathbb R^n$ \ $ A $ is never convex.

So far I get that considering $p,q \in \mathbb R^n$ convex, $\lambda p + (1- \lambda)q \in \mathbb R^n$, and removing $A$ from it will make no difference if $p,q$ aren't part of the set $A$. Is it enough?

Answer 1

The straight line divides the plane into two complementary convex sets. In general, the same holds for a hyperplane.