Charts & Visual Data
Venn Diagram Overlap Formula: 2- & 3-Set Inclusion-Exclusion Union & Exclusive Counts
Reconcile audience or SKU overlaps across three overlapping sets using the Principle of Inclusion-Exclusion so Venn diagram region labels and unique-reach totals never double-count intersections.
Prevent double-subtraction errors in 3-circle Venn diagrams!
When mapping cross-channel reach across Email (|A| = 520), Mobile App (|B| = 380), and Loyalty Card (|C| = 290), subtracting all three pairwise overlaps |A n B| + |A n C| + |B n C| removes customers in the triple center |A n B n C| three times instead of twice! By Poincaré’s Principle of Inclusion-Exclusion, exact deduplicated union reach is |A U B U C| = |A| + |B| + |C| - |A n B| - |A n C| - |B n C| + |A n B n C|!
Similarly, the exclusive Email-Only outer crescent is NOT |A| - |A n B| - |A n C|, which undercounts by |A n B n C|, but |A_only| = |A| - |A n B| - |A n C| + |A n B n C|!
| Venn Region (|A|=520, |B|=380, |C|=290) | Inclusion-Exclusion Formula | Exact Region Count |
|---|---|---|
| Email-Only Crescent A \ (B U C) | 520 - 140 - 110 + 45 | 315 |
| Pairwise-Only Lenses (AB\C, AC\B, BC\A) | (140-45), (110-45), (95-45) | 95, 65, 50 |
| Total Deduplicated Union |A U B U C| | 520 + 380 + 290 - 140 - 110 - 95 + 45 | 890 unique customers |
Three-Set Deduplicated Union Reach |A U B U C| with Overlap Consistency Guard
Applies Inclusion-Exclusion across B2:B8 while rejecting impossible inputs where triple overlap B8 exceeds any pairwise intersection.
=IF(OR(B8 < 0, B8 > MIN(B5:B7), B5 > MIN(B2, B3), B6 > MIN(B2, B4), B7 > MIN(B3, B4)), "Impossible Set Intersection Bounds", B2 + B3 + B4 - B5 - B6 - B7 + B8)Exclusive Set-A-Only Crescent Count |A \ (B U C)|
Adds back triple intersection B8 after subtracting pairwise overlaps B5 and B6 from B2.
=B2 - B5 - B6 + B8Try the example
Use the original values or change them to test your understanding.