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.
Description
Two sets divide a universe into four membership regions.
Two sets divide a universe into four membership regions. The intersection and the region outside both sets are as significant as either exclusive region.1
The tool returns regionIndex, region. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Venn Diagram Two-Set Region Number Mapper (0-3)
Use this for the following task: Map two Boolean set memberships to a Venn region using A as the most significant bit. Prepare the specified logical encoding before running the check or transformation.
How to use Venn Diagram Two-Set Region Number Mapper (0-3) 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 according to the field table, then run the tool.
- Read regionIndex, region. 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 |
Supply membership flags for a single object. Encode A as the more significant bit and return the corresponding intersection, a-only, b-only or outside label.
region index = 2×inA+inB 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 |
| region | Venn region | string |
{
"input": {
"inA": true,
"inB": true
},
"output": {
"regionIndex": 3,
"region": "intersection"
}
}Limitations and assumptions
Membership must already be known. No elements, set cardinalities or overlap areas are calculated.
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 Three-Set Region Number Mapper (0-7) when you need its operation: Map three Boolean set memberships to a Venn region index and the list of containing sets. Choose Square of Opposition Contradictory Pair Mapper (A-O, E-I) for the complementary operation: Map a categorical proposition to its contradictory form for the same subject and predicate.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- 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.
- Square of Opposition Contradictory Pair Mapper (A-O, E-I)
Map a categorical proposition to its contradictory form for the same subject and predicate.