XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker
Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs.
Description
Exclusive OR is true when exactly one of two propositions is true.
Exclusive OR is true when exactly one of two propositions is true. Its ordinary OR-and-NOT expansion distinguishes exclusivity from inclusive disjunction.1
The tool returns xor, expanded. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) Checker
Use this for the following task: Evaluate XOR and its classical conjunction/disjunction expansion on two Boolean inputs. Prepare the specified logical encoding before running the check or transformation.
How to use XOR Definition Expansion (¬P∧Q)∨(P∧¬Q) 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 xor, 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 inequality of the two values and separately calculate the OR-and-NOT expansion, returning both truth values.
p XOR q ≡ (p OR q) AND NOT(p AND q) The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| xor | Xor | boolean |
| expanded | Expanded | boolean |
{
"input": {
"p": true,
"q": false
},
"output": {
"xor": true,
"expanded": true
}
}Limitations and assumptions
This checks one supplied assignment. Text such as "false" is not a Boolean input.
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 XNOR Equality Gate Definition Checker when you need its operation: Evaluate XNOR equality and its classical matching-state expansion on two Boolean inputs. Choose Half Adder Sum Carry Boolean Pair Checker for the complementary operation: Compute the Boolean sum and carry bits of a half adder.
Background reference: Complete truth tables.
References
-
Complete truth tables — forallx Calgary, Open Logic Project
Similar or alternative tools
- XNOR Equality Gate Definition Checker
Evaluate XNOR equality and its classical matching-state expansion on two Boolean inputs.
- Half Adder Sum Carry Boolean Pair Checker
Compute the Boolean sum and carry bits of a half adder.