Convex hull of less than 3 points
It's true for a one set point. The set is convex, and it is the "smallest" convex set containing the point, so it is the convex hull.
For a two set point, the convex hull is simply the line segment connecting the 2 points. Remember the definition of a convex set: With 2 points in the set, any point on their connecting line segment has to be in it as well. So the connecting line segment has to be in the convex hull, and since the line segment is convex, it is the convex hull.
The empty set itself is convex, so the convex hull of it is the empty set itself again.