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Consider the following two well-formed formulas in prepositional logic.

$F1 : P \Rightarrow \neg P$

$F2: (P \Rightarrow \neg P) \vee (\neg P \Rightarrow P)$

Which of the following statements is correct?

  1. $F1$ is Satisfiable, $F2$ is valid
  2. $F1$ is unsatisfiable, $F2$ is Satisfiable
  3. $F1$ is unsatisfiable,  $F2$ is valid
  4. $F1$ and $F2$ both are Satisfiable
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Answer (1)

F1 evaluates to P' which is true at P = 0. However, at P = 1, it is equal to 0. Thus, F1 is satisfiable but not valid

F2 evalautes to 1 (valid) irrespective of the value of P.
Answer:

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