GATE CSE 2001 | Question: 1.3

Question

Consider two well-formed formulas in propositional logic

$F_1: P \Rightarrow \neg P$          $F_2: (P \Rightarrow \neg P) \lor ( \neg P \Rightarrow P)$

Which one of the following statements is correct?

• A. $F_1$ is satisfiable, $F_2$ is valid
• B. $F_1$ unsatisfiable, $F_2$ is satisfiable
• C. $F_1$ is unsatisfiable, $F_2$ is valid
• D. $F_1$ and $F_2$ are both satisfiable

Comments

If this question would be MSQ, then option A) and D), both are correct.

---

I too think of the same think because a tautology is also satisfiable.. can any one correct me if i am wrong … My reasoning is the satisfiable wants at least one input combination for which the output is true ..  and tautology give output true for all input combination of inputs ..

---

Well we can solve this easily by the case method or by the boolean algebra

Answer 1

I can see both are satisfiable i wl go for option b

Comments

valid means always true. That is, whatever be the values assigned to the variables, the formula returns true. eg. $p\vee \neg p$

---

Then what is your opinion about this which is the most appropriate

---

(a) is the most appropriate.