Convex

Hey,

I have a few questions about convex and non-convex:

Is a set sonsisting of only 2 points convex?

If a single point is removed from line, do the remaining points form a convex set?

Does a ray seperate a plane?

Any help is appreciated.

Is a set consisting of only 2 points convex?
NO! The two points determine a line segment; the midpoint is not in the set.

If a single point is removed from line, do the remaining points form a convex set?
YES. It is by default; the definition is vacuous. There are no two points in the set.

Does a ray separate a plane?
NO! A line separates a plane. A ray is a half-line with an endpoint.