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GATE | GATE-CS-2001 | Question 3

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Consider two well-formed formulas in prepositional logic. 

F1 : P ⇒ ¬P
F2 : ( P⇒¬P)∨(¬P⇒P)

Which of the following statements is correct? 
 

(A)

F1 unsatisfiable, F2 is satisfiable

(B)

F1 and F2 are both satisfiable

(C)

F1 is unsatisfiable, F2 is valid 

(D)

F1 is satisfiable, F2 is valid



Answer: (D)

Explanation:

The concept behind this solution is: 
a) Satisfiable 
If there is an assignment of truth values which makes that expression true. 
b) UnSatisfiable 
If there is no such assignment which makes the expression true 
c) Valid 
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) = 
Tautology 
So, F1 is Satisfiable and F2 is valid 
Option (d) is correct. 
 


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Last Updated : 11 Oct, 2021
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