Equality of Voronoi diagram

It's easy to see that you can't say that A = B. Consider 2 points. The Voronoi diagram consists of a single line(the perpendicular bisector of the 2 points). There are infinite pairs of points having the same perpendicular bisector. If all the points are distinct, the sizes of the sets would be equal. Since, each region in the Voronoi diagram corresponds to exactly 1 point from the set, the sizes of the sets must be equal.