De Morgan OR-to-AND Negation Transformer
Rewrite a negated disjunction of two identifier atoms using ! for negation and && for conjunction.
Description
De Morgan’s law moves negation across a disjunction by negating each operand and changing the connecting operation.
De Morgan’s law moves negation across a disjunction by negating each operand and changing the connecting operation.1
The tool returns original, rewritten. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use De Morgan OR-to-AND Negation Transformer
Use this for the following task: Rewrite a negated disjunction of two identifier atoms using ! for negation and && for conjunction. Prepare the specified logical encoding before running the check or transformation.
How to use De Morgan OR-to-AND Negation Transformer 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 original, rewritten. 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 | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
| q | Q | string; maximum text length 100; pattern ^(?!(?:true|false)$)[A-Za-z_][A-Za-z0-9_]*$(?![\s\S]) | Required |
Supply identifier atoms p and q. Return the fixed original negated binary expression and the corresponding De Morgan expansion.
NOT(P OR Q) ≡ 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 |
|---|---|---|
| original | Original propositional formula | string (propositional-formula) |
| rewritten | Equivalent propositional formula | string (propositional-formula) |
{
"input": {
"p": "p",
"q": "q"
},
"output": {
"original": "!(p || q)",
"rewritten": "(!p && !q)"
}
}Limitations and assumptions
Operands are case-sensitive identifier atoms, not complete expressions. The tool does not parse a proof or determine whether the premises are true.
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 De Morgan AND-to-OR Negation Transformer when you need its operation: Rewrite a negated conjunction of two identifier atoms using ! for negation and || for disjunction. Choose Material Implication to Disjunction Rewriter (P→Q ≡ ¬P∨Q) for the complementary operation: Rewrite material implication between identifier atoms as a disjunction with a negated antecedent.
Background reference: Additional rules for TFL.
References
-
Additional rules for TFL — forallx Calgary, Open Logic Project
Similar or alternative tools
- De Morgan AND-to-OR Negation Transformer
Rewrite a negated conjunction of two identifier atoms using ! for negation and || for disjunction.
- Material Implication to Disjunction Rewriter (P→Q ≡ ¬P∨Q)
Rewrite material implication between identifier atoms as a disjunction with a negated antecedent.