The proposition ¬q ∨ p is logically equivalent to:
2011
The proposition ¬q ∨ p is logically equivalent to:
Answer: B. q → p — ConceptMaterial implication follows the identity A → B ≡ ¬A ∨ B. An implication is rewritten by negating its antecedent and joining that result to its…
- A.
p → q
- B.
q → p
- C.
p ↔ q
- D.
p ∨ q
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Correct answer: B
Concept
Material implication follows the identity A → B ≡ ¬A ∨ B.
An implication is rewritten by negating its antecedent and joining that result to its consequent with OR.
Application
Compare ¬q ∨ p with the standard form ¬A ∨ B.
Taking A = q and B = p gives q → p ≡ ¬q ∨ p.
Cross-check
Both ¬q ∨ p and q → p are false only in the case q = true and p = false; their truth values therefore agree in every case.
Hence, the equivalent proposition is q → p.
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