Consider two well-formed formulas in prepositional logic. P⇒¬P)∨(¬P⇒P) Which of
2001
Consider two well-formed formulas in propositional logic.
F1: P ⇒ ¬P
F2: (P ⇒ ¬P) ∨ (¬P ⇒ P)
Which of the following statements is correct?
- A.
F1 unsatisfiable, F2 is satisfiable
- B.
F1 and F2 are both satisfiable
- C.
F1 is unsatisfiable, F2 is valid
- D.
F1 is satisfiable, F2 is valid
Attempted by 21 students.
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Correct answer: D
For F1: P ⇒ ¬P is equivalent to ¬P ∨ ¬P, which simplifies to ¬P.
So F1 is true when P is false, and false when P is true. Hence, F1 is satisfiable but not valid.
For F2: (P ⇒ ¬P) ∨ (¬P ⇒ P).
Here, P ⇒ ¬P is equivalent to ¬P, and ¬P ⇒ P is equivalent to P.
Therefore, F2 is equivalent to ¬P ∨ P, which is always true. Hence, F2 is valid.
So F1 is satisfiable and F2 is valid. Hence, option D is correct.