The question is:
The propositional function (~(P V Q) V (~P ^ Q) V P) is: [NOTE: "^" means "AND" and "~" means "Negation".The problem should be solved without truth tables]
a)Tautology b) Contradiction c) Contingency d)<=>P
I solved the question in below way:
STEP-1: I considered (~(P V Q) V (~P ^ Q)) as A and P as B.
STEP-2: I assumed the given function to be contrdiction and tried to prove (A V B) as false.
STEP-3:To make (A V B) to be false, make A and B both false.So,I considered P as false and substituted all the values of P in A as false.
STEP-4:Next,I assumed Q to be true in A.
STEP-5:When I finally solved by substituting T and F in A,I got A as T and B is F.Since (T V F) is T ,I assumed above propositional function to be tautology.
My doubt starts here.
Similarly,following the above mentioned steps,if I substitute B as true,Iam getting (A V B) as false.(i.e (~(P V Q) V (~P ^ Q)) as false).It should be contingency then.
But, the answer is given as A.
Please help?What is the answer A or C.