Consider the following two well-formed formulas in prepositional logic.
F1 : P ⇒ ¬ P F2 : (P ⇒ ¬ P) ∨ (¬ P ⇒ P)
Which of the following statements is correct?
(A) F1 is Satisfiable, F2 is valid
(B) F1 is unsatisfiable, F2 is Satisfiable
(C) F1 is unsatisfiable, F2 is valid
(D) F1 and F2 both are Satisfiable
P → ¬P
= ¬P(¬P) + P¬(¬P)
= ¬P + P is satisfiable.
(P ⇒ ¬ P) ∨ (¬ P ⇒ P)
= (¬P(¬P) + P¬(¬P)) v (P¬(¬P) + ¬P(¬P) )
= satisfiable v satisfiable
So, option (A) is correct.
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