XNOR Equality Gate Definition Checker
Evaluate XNOR equality and its classical matching-state expansion on two Boolean inputs.
Description
XNOR expresses equality of two Boolean truth states.
XNOR expresses equality of two Boolean truth states. Both true and both false satisfy its expansion into two conjunctions.1
The tool returns xnor, expanded. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use XNOR Equality Gate Definition Checker
Use this for the following task: Evaluate XNOR equality and its classical matching-state expansion on two Boolean inputs. Prepare the specified logical encoding before running the check or transformation.
How to use XNOR Equality Gate Definition Checker 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 p, q according to the field table, then run the tool.
- Read xnor, expanded. 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 |
|---|---|---|---|
| p | P | boolean | Required |
| q | Q | boolean | Required |
Supply Boolean p and q. Calculate strict equality of the input values and separately calculate the both-true-or-both-false expansion. Return both truth values.
p XNOR q ≡ (p AND q) OR (NOT p AND NOT q) The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| xnor | Xnor | boolean |
| expanded | Expanded | boolean |
{
"input": {
"p": true,
"q": true
},
"output": {
"xnor": true,
"expanded": true
}
}Limitations and assumptions
The output concerns the supplied truth values rather than logical equivalence of arbitrary formulas.
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 XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker when you need its operation: Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs. Choose Material Equivalence Expansion Rewriter (P↔Q two forms) for the complementary operation: Expand material equivalence between identifier atoms into the disjunction of their matching truth states.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker
Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs.
- Material Equivalence Expansion Rewriter (P↔Q two forms)
Expand material equivalence between identifier atoms into the disjunction of their matching truth states.