UGC NET CSE | November 2017 | Part 3 | Question: 59

Question

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?

• 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

Comments

ans is 1

Answer 1

https://gateoverflow.in/696/gate2001-1-3

Answer 2

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.