GATE | GATE-CS-2001 | Question 3
Which 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
Explanation: The concept behind this solution is:
If there is an assignment of truth values which makes that expression true.
If there is no such assignment which makes the expression true
If the expression is Tautology
Here, P => Q is nothing but –P v Q
F1: P => -P = -P v –P = -P
F1 will be true if P is false and F1 will be false when P is true so F1 is Satisfiable
F2: (P => -P) v (-P => P) which is equals to (-P v-P) v (-(-P) v P) = (-P) v (P) =
So, F1 is Satisfiable and F2 is valid
Option (a) is correct.
This solution is contributed by Anil Saikrishna Devarasetty.