Multiple choice

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?

  1. ((P ∨ R) ∧ (Q ∨ ¬R)) ⇒ (P ∨ Q) is logically valid

  2. (P ∨ Q) ⇒ ((P ∨ R)) ∧ (Q ∨ ¬R)) is logically valid

  3. (P ∨ Q) is satisfiable if and only if (P ∨ R) ∧ (Q ∨ ¬R) is satisfiable

  4. (P ∨ Q) ⇒ FALSE if and only if both P and Q are unsatisfiable
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If P = True, Q = False, R = True Then, we find (T$\cup F$)$\Rightarrow$(T$\cup$T) $\land$(F$\cup$F) T$\Rightarrow$(T$\land$F) T$\Rightarrow$F F$\cup$F False is not valid.

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