The conditional 'if not p then q' is logically equivalent to 'p or q'
Is it true that the conditional 'if not p then q' is logically equivalent to 'p or q'?
The logical equivalence between the material conditional 'if not p then q' and 'p or q' is a foundational theorem of classical propositional logic, representing a basic definition that requires no empirical citation.
Verdict: COMMON KNOWLEDGE · 0 sources for, 0 against · Last checked
The claim states a fundamental, definitional equivalence in classical propositional logic (material implication: thet ¬p → q is equivalent to p ∨ q). By definition, this is common knowledge in logic and mathematics, requiring no external empirical validation or literature citations. Therefore, STEP 0 classifies it as COMMON_KNOWLEDGE.
- Is it true that if P then Q and Q only if P are logically equivalent statements? SUPPORTED
- Is it true that epistemology is logically equivalent to formal logic? REFUTED
- Is it true that scientific explanations are logically equivalent to deductive entailments? SUPPORTED
- Is it true that the first and second formulations of Kant's categorical imperative are logically equivalent? SUPPORTED
- Is it true that P <-> Q and P -> ~Q logically entails a contradiction? COMMON KNOWLEDGE
- Is it true that Forward scattering is equivalent to no scattering? REFUTED
What does the evidence say?
The claim states a fundamental, definitional equivalence in classical propositional logic (material implication: thet ¬p → q is equivalent to p ∨ q). By definition, this is common knowledge in logic and mathematics, requiring no external empirical validation or literature citations. Therefore, STEP 0 classifies it as COMMON_KNOWLEDGE.
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