Identity Law Neutral Element Checker (P∧T, P∨F)
Check whether a Boolean constant is the identity element of conjunction or disjunction.
Description
An identity element leaves a Boolean operand unchanged.
An identity element leaves a Boolean operand unchanged. True is neutral for conjunction and false is neutral for disjunction.1
The tool returns neutral. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Identity Law Neutral Element Checker (P∧T, P∨F)
Use this for the following task: Check whether a Boolean constant is the identity element of conjunction or disjunction. Prepare the specified logical encoding before running the check or transformation.
How to use Identity Law Neutral Element Checker (P∧T, P∨F) 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 operator, constant according to the field table, then run the tool.
- Read neutral. 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 |
|---|---|---|---|
| operator | Boolean operator | string; choices "and", "or" | Required |
| constant | Candidate identity | boolean | Required |
Choose and or or and supply a Boolean candidate constant. Return the constant itself for and or its negation for or as the neutral flag.
AND identity = true; OR identity = false The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| neutral | Neutral | boolean |
{
"input": {
"operator": "and",
"constant": true
},
"output": {
"neutral": true
}
}Limitations and assumptions
No expression is rewritten. A false result only means the candidate is not the chosen operation’s identity.
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 Domination Law Annihilator Checker (P∨T=T, P∧F=F) when you need its operation: Check whether a Boolean constant is the annihilator of conjunction or disjunction. Choose Idempotence Duplicate Term Collapser Checker (P∧P=P) for the complementary operation: Collapse equal identifier operands under conjunction or disjunction using idempotence.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- Domination Law Annihilator Checker (P∨T=T, P∧F=F)
Check whether a Boolean constant is the annihilator of conjunction or disjunction.
- Idempotence Duplicate Term Collapser Checker (P∧P=P)
Collapse equal identifier operands under conjunction or disjunction using idempotence.