Let F be a finite collection of halfplanes covering the plane. Prove that there are three halfplanes of F covering the plane.
So I understand that half-planes are formed when a line divides the plane resulting in either right or left half-plane(if vertically) or upper and lower half-plane (if horizontally). So I see that there are three parts i.e. the line dividing the plane and the two half-planes that forms. So according to the definition itself any multiple line division(let's say vertical division) will always result in right and left half-planes. But how do I prove it? Is my approach correct?