Commutativity Applicability Checker for AND/OR

Classical pure Boolean commute identity witness for AND/OR; not short-circuit side-effect equivalence or arbitrary programming operator.

Description

Commutativity Applicability Checker for AND/OR: return identity holds.

Commutativity exchanges the order of two operands. Boolean AND and OR are commutative operations.

This tool returns identity holds. Use the stated units and model convention when interpreting these fields.

When to use this tool

Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.

Check the supported input and output contract against an existing calculation or observation.
Use the complete example to confirm units, selector spelling and result interpretation.

How to use the tool and how it works

Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
Run the tool. Correct input errors before interpreting an output.
Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.

Evaluate the selected operation for (a,b) and (b,a), and report whether their Boolean results agree.^[1]

Input field	Meaning and units	Accepted input
operator	Operator.	Exact value: "AND", "OR"
a	A.	true or false
b	B.	true or false

Output field	Interpretation
result	Object containing the following named result fields.
result.identityHolds	Identity holds flag under the exact conditions described above.

json

{
  "input": {
    "operator": "AND",
    "a": true,
    "b": false
  },
  "output": {
    "result": {
      "identityHolds": true
    }
  }
}

Limitations and assumptions

Only the two supported operators and supplied truth values are evaluated.
Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.

Alternative or Complementary methods

Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.

References

Tool behavior and example: Commutativity Applicability Checker for AND/OR — tool.io

Similar or alternative tools

a proposition classifier
Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative.
absorption law simplifier
Absorption removes a nested combination that adds no new truth condition to its repeated leading atom.