Gate Question for CSE 1995 In Propositional logic

Question

I have an question regarding Propositional Logic,

(! = NOT, V = OR, -> = Implication)

If the proposition !p -> q is true, then the truth value of the proposition !p V (p -> q) is,

1. true 2. multiple valued, 3. false, 4. cannot be determinded

now from the truth table for !p V (p->q) i get 1 1 0 1 which means it is neither true nor false.

so the answer would be either 2 or 4 and the actual answer is 4.

My question is what does 'multiple valued' means in this case? is it just there to misdirect or is there any logic behind it? or am i doing this completely wrong?

Please any kind of advice would appreciated!!!

Answer 1

Answer is option D

Answer 2

$!p\rightarrow q$ being true  means that q is not false when p is false.

Then we only have three combination:
T T = $F\vee (T\rightarrow T) = T$
T F = $F\vee (T\rightarrow F) = F$
F T = $T\vee (F\rightarrow T) = T$

Hence can't be true or false. So no 1 or 3.

Multiple valued means that there are some other logical variable available for use besides True and False or 0 and 1. Like in fuzzy logic. Since, we are not dealing with those, I don't think that option will ever be reasonable to mark. You need to bring in someone experienced here for more clarification but I think I am right.

Comments

Please explain what does multiple valued means here????