UGC-NET | UGC-NET CS 2017 Nov – III | Question 59

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


Answer: (A)

Explanation: F1:
P → ¬P
= ¬P(¬P) + P¬(¬P)
= ¬P + P is satisfiable.
F2:
(P ⇒ ¬ P) ∨ (¬ P ⇒ P)
= (¬P(¬P) + P¬(¬P)) v (P¬(¬P) + ¬P(¬P) )
= satisfiable v satisfiable
is satisfiable.
So, option (A) is correct.


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