Consider two well-formed formulas in propositional logic F₁: P ⇒ ¬P F₂: (P ⇒…
2001
Consider two well-formed formulas in propositional logic
F₁: P ⇒ ¬P
F₂: (P ⇒ ¬P) ∨ (¬P ⇒ P)
Which one of the following statements is correct?
- A.
F₁ is satisfiable, F₂ is valid
- B.
F₁ unsatisfiable, F₂ is satisfiable
- C.
F₁ is unsatisfiable, F₂ is valid
- D.
F₁ and F₂ are both satisfiable
Attempted by 16 students.
Show answer & explanation
Correct answer: A
F₁: P ⇒ ¬P is equivalent to ¬P ∨ ¬P = ¬P. it is satisfiable.
F₂: (P ⇒ ¬P) ∨ (¬P ⇒ P) = ¬P ∨ P, which is a tautology. Therefore F₂ is always true regardless of P's value.
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