GATE CSE 1990 | Question: 3-x

Question

Indicate which of the following well-formed formulae are valid:

• A. $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$
• B. $\left(P\Rightarrow Q\right) \Rightarrow \left( \neg P \Rightarrow \neg Q\right)$
• C. $\left(P{\wedge} \left(\neg P \vee  \neg Q\right)\right) \Rightarrow Q$
• D. $\left(P \Rightarrow R\right) \vee \left(Q \Rightarrow R\right) \Rightarrow \left(\left(P \vee Q \right)  \Rightarrow R\right)$

Comments

That's fine:)

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@Arjun Sir, Is there any difference between "⇒" and "->" (Double arrow and Single arrow) ? In the new questions they are using single arrow only for implication, I read it somewhere that double arrow is actually used to say that something's a tautology 

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In option D if R=F then this option also valid

But if Q,R=F then this is not valid

Because If take rhs false then lhs become true over all false so invalid

Answer 1

(A) option is correct

Solution:

Answer 2

the same idea as in  answer by Tuhin but with the different format

An argument is valid if we cannot make all premises true and the conclusion false without getting contradiction

An argument is invalid if can make all premises true and the conclusion false.