The following resolution rule is used in logic programming.
Derive clause (P$\lor$Q) from clauses (P $\lor$ R), (Q$\lor$$\neg$R)
Which of the following statements related to this rule is FALSE?
-
((P $\lor$ R) $\land$ (Q $\lor$ $\neg$R)) _ (P $\lor$ Q) is logically valid
-
(P $\lor$ Q) $\Rightarrow$ ((P $\lor$ R) $\land$ (Q $\lor$ $\neg$R)) is logically valid
-
(P $\lor$ Q) is satisfiable if and only if (P $\lor$ R) Ù (Q $\lor$ $\neg$R) is satisfiable
-
(P $\lor$ Q) $\Rightarrow$ FALSE if and only if both P and Q are unsatisfiable
B
Correct answer
Explanation
If P = True, Q = false, R =True
Then we find,
(T$\cup$F) $\Rightarrow$((T$\cup$T)$\lor$ (F$\cup$F)
T $\Rightarrow$((T$\lor$F)
T $\Rightarrow$F
F$\cup$F = False(is not valid)