Work out venn diagram (3 sets) instantly with clear inputs, formula shown and shareable results.
For three sets inclusion-exclusion alternates signs: add the singles, subtract the pairs, add the triple back. Region counts follow from the same principle, for example A only = |A| − |A∩B| − |A∩C| + |A∩B∩C|.
Three-set inclusion-exclusion
|A∪B∪C| = |A|+|B|+|C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|
30 + 25 + 20 − 10 − 8 − 6 + 3 = 54, leaving 6 outside all three in a universe of 60.
Subtracting all three pairwise overlaps removes the central region three times after it was added three times, so it must be restored once.