Venn Diagram Three-Set Region Number Mapper (0-7)
Map three Boolean set memberships to a Venn region index and the list of containing sets.
Description
Three sets divide a universe into eight membership regions, including the region outside all three.
Three sets divide a universe into eight membership regions, including the region outside all three. A binary code gives each region a reproducible identifier.1
The tool returns regionIndex, membershipBits, memberOf. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Venn Diagram Three-Set Region Number Mapper (0-7)
Use this for the following task: Map three Boolean set memberships to a Venn region index and the list of containing sets. Prepare the specified logical encoding before running the check or transformation.
How to use Venn Diagram Three-Set Region Number Mapper (0-7) and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter inA, inB, inC according to the field table, then run the tool.
- Read regionIndex, membershipBits, memberOf. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| inA | In A | boolean | Required |
| inB | In B | boolean | Required |
| inC | In C | boolean | Required |
Supply three Boolean membership flags. Return the ABC bit string, integer index and ordered list of sets containing the object.
region index = 4×inA+2×inB+inC The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| regionIndex | Binary region index | integer |
| membershipBits | Membership bits in A, B, C order | string (binary) |
| memberOf | Containing sets | list of string |
{
"input": {
"inA": true,
"inB": false,
"inC": true
},
"output": {
"regionIndex": 5,
"membershipBits": "101",
"memberOf": [
"A",
"C"
]
}
}Limitations and assumptions
This maps one object’s supplied membership. It does not draw a Venn diagram or infer membership from data.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Venn Diagram Two-Set Region Number Mapper (0-3) when you need its operation: Map two Boolean set memberships to a Venn region using A as the most significant bit. Choose Categorical Syllogism Mood-Figure Label Parser (EAE-1 etc.) for the complementary operation: Parse a categorical mood and figure such as AAA-1 into proposition kinds and standard S, M, and P term positions.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- Venn Diagram Two-Set Region Number Mapper (0-3)
Map two Boolean set memberships to a Venn region using A as the most significant bit.
- Categorical Syllogism Mood-Figure Label Parser (EAE-1 etc.)
Parse a categorical mood and figure such as AAA-1 into proposition kinds and standard S, M, and P term positions.