Description
Calculate onlyA=a-ab-ac+abc and feasible from its nonnegativity and the supplied pair/triple intersection bounds.
A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.
Calculate onlyA=a-ab-ac+abc and feasible from its nonnegativity and the supplied pair/triple intersection bounds.
When to use this tool
Use Three Set Venn Region Cardinality Term when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.
How to use the tool and how it works
- Enter a, ab, ac, abc. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read onlyA, feasible. Inspect feasible before interpreting the associated values.
Calculate onlyA=a-ab-ac+abc and feasible from its nonnegativity and the supplied pair/triple intersection bounds. Require nonnegative integer counts.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Safe integer. |
| ab | Ab | Required. Safe integer. |
| ac | Ac | Required. Safe integer. |
| abc | Abc | Required. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| onlyA | A-only region count; negative values can be reported with feasible false. | Required. Safe integer. |
| feasible | Whether the stated count or denominator conditions hold. | Required. Boolean. |
{
"input": {
"a": 20,
"ab": 8,
"ac": 6,
"abc": 3
},
"output": {
"onlyA": 9,
"feasible": true
}
}Limitations and assumptions
- Negative onlyA is returned with feasible false. This checks one A-related Venn region, not global feasibility of a complete three-set diagram or actual membership.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.
References
Similar or alternative tools
- set/union
Return unique strings from two lists in first-occurrence order.
- Set Inclusion Exclusion One Region Term
Use coefficient one for odd memberships and minus one for even, returning coefficient*regionCardinality.