Set Operations Explorer: 2D Venn Diagrams

Set theory's core operations — union, intersection, difference and symmetric difference — are usually drawn as flat two-circle Venn diagrams, and this simulator makes that classic picture fully interactive. Two overlapping circles of glowing points represent sets A and B; 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. A live bar chart panel breaks down the count in each of the four disjoint regions (A-only, B-only, overlap, and the currently excluded elements) while the inclusion-exclusion formula and cardinalities |A|, |B|, |A ∩ B| and |A ∪ B| update alongside it. Drag the diagram to pan and scroll to zoom in on any region.