Set Operations Explorer: 3D Venn Diagrams

Set theory's core operations — union, intersection, difference and symmetric difference — are usually drawn as flat two-circle Venn diagrams. This simulator renders them as real 3D point clouds: two overlapping spheres of glowing spheres, one per set, where the lens-shaped overlap region holds the shared elements. Adjust the size of each set and how much they overlap, then pick an operation to see the exact resulting subset light up while every excluded element fades to gray, with the inclusion-exclusion formula and live cardinalities |A|, |B|, |A ∩ B| and |A ∪ B| updating alongside it.