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Mathematics

Three sets and their overlaps

Split counts for three groups into seven separate regions and find how many people lie outside all three groups.

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01

Your inputs

The starting values are an example.

Decimals: 12.5 · Thousands: 1,234.56. Follow the field instructions for lists.

02

Your result

Enter your values and select Calculate.

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Your result will include the relevant values and units.

Understand the calculation

Formula and example

How it is calculated

|A∪B∪C|=|A|+|B|+|C|−|A∩B|−|A∩C|−|B∩C|+|A∩B∩C|.

Worked example

For A=40, B=35, C=30, AB=15, AC=10, BC=12 and ABC=5, 73 out of 100 people belong to at least one set; 27 belong to none.

Things to check

  • Pairwise intersections always include the people in all three sets.
  • Contradictory counts that produce negative regions are rejected. All counts refer to the same population.

Frequently asked questions

How does A and B differ from “only A and B”?

A and B includes members of C. Subtract the triple intersection to obtain the exclusive region.