Inclusion-Exclusion Calculator

This calculator applies the inclusion-exclusion principle to three overlapping sets: |A∪B∪C| = |A| + |B| + |C| − |A∩B| − |B∩C| − |A∩C| + |A∩B∩C| (line 13). |A| (Set A Size) has the largest measured effect on the Union at the calculator's defaults, simply because it's the largest of the three set sizes (100, versus 80 for B and 60 for C) — a proportional nudge to a bigger starting number produces a bigger absolute swing in a formula that adds all three linearly. The three pairwise intersections are each subtracted once, so raising any of them pulls the Union down — but the triple intersection |A∩B∩C| is added back at the end, so raising it alone actually pushes the Union up, the opposite direction from the pairwise terms. That "+" exists because the standard sum-then-subtract-pairs approach subtracts the triple-overlap region three times over (once inside each pairwise term), so it has to be added back once to land on the correct count — not because more triple-overlap intuitively means a bigger union.

Exclusive to A, B, and C each report the count of elements belonging to only that one set, none of the others. The calculator does not check that the seven numbers you enter actually describe a consistent configuration of three real sets — it plugs whatever you type straight into the formula (line 13) and reports the result even if, say, an intersection is larger than the sets it's supposed to be part of.