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The union is the number that belongs to at least one set. With N, outside all sets = N − union.
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Examples
Use exact regions for 2–3 sets when you know the separate areas in a Venn diagram. Use intersections when you know total set and overlap counts.
How to use inclusion-exclusion
Adding |A| and |B| counts A∩B twice, so the overlap is subtracted once. With three sets, the triple intersection is then removed too many times, so it is added back.
- Typical uses include multi-select surveys, overlapping class groups, and deduplicating audience or report segments.
- Independence is a different assumption: inclusion–exclusion itself only corrects overlap counts.
- Mixing Venn region counts with total intersection counts changes the meaning of the fields, so choose one input format and use it consistently.
FAQ
What is the inclusion–exclusion principle?
It counts a union by adding single-set sizes, subtracting pairwise intersections, adding triple intersections, and continuing with alternating signs.
How do I calculate “A or B”?
For two sets, |A∪B| = |A| + |B| − |A∩B|. The calculator evaluates this after all required fields are valid.
What is the difference between an exact region and an intersection?
“A∩B” includes items that may also belong to other sets. “A∩B only” excludes every other set. Do not mix the two meanings in one input format.
Why is an inconsistency error shown?
An intersection cannot be larger than a set that contains it, and every derived exact region must be non-negative. If either rule fails, the inputs cannot represent real sets.
Is independence the same as inclusion–exclusion?
No. Independence is a probability assumption that may help determine intersections. Inclusion–exclusion is the counting rule used once the overlaps are known.
How do I calculate items outside all sets?
Enter the universal-set size N. The calculator uses outside all sets = N − union and shows probabilities when N is positive.