Set Theory Calculator

This calculator derives every standard two-set relationship — union, intersection, the two one-way differences, symmetric difference, and both complements — from just three cardinalities: Set A Size, Set B Size, and the Overlap (A ∩ B) between them. Union (A ∪ B) is setASize + setBSize − overlapCount (line 13), so Set A Size is the single strongest driver of it at the calculator's defaults — a 10% nudge to Set A Size (50) is 5, while the same 10% nudge to Set B Size (30) is only 3, so Set A Size moves Union about 1.7 times as much simply because its default value is larger; with equal-sized sets, the two inputs would move Union equally. Increasing the Overlap, by contrast, pulls Union down, since a larger shared region means fewer elements are being counted twice.

Universal Set Size never enters the Union formula at all; it only affects Complement of A and Complement of B, and the engine silently raises it to at least setASize + setBSize − overlapCount (line 7-10) if you type a smaller value, rather than rejecting the entry. Overlap Count itself is clamped to never exceed the smaller of the two set sizes (line 6), since a shared region can't be larger than either set it belongs to. This calculator only models two sets — it has no way to represent a three-way (or higher) overlap, such as a three-circle Venn diagram, where the pairwise overlap counts alone aren't enough to determine how much of all three sets intersect at once.