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GATE | GATE-CS-2003 | Question 72

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  • Last Updated : 21 Aug, 2018

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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