GATE | GATE-CS-2003 | Question 72
The following resolution rule is used in logic programming.
Derive clause (P ∨ Q) from clauses (P ∨ R), (Q ∨ ¬R)
Which of the following statements related to this rule is FALSE?
(A) ((P ∨ R) ∧ (Q ∨ ¬R)) ⇒ (P ∨ Q) is logically valid
(B) (P ∨ Q) ⇒ ((P ∨ R)) ∧ (Q ∨ ¬R)) is logically valid
(C) (P ∨ Q) is satisfiable if and only if (P ∨ R) ∨ (Q ∨ ¬R) is satisfiable
(D) (P ∨ Q) ⇒ FALSE if and only if both P and Q are unsatisfiable
Answer: (A)
Explanation: Option (A) itself is definition of resolution.
So option (A) is correct.
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