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March 21, 2024Question 14215 – Propositional-Logic
Let p and q be two propositions. Consider the following two formulae in propositional logic.
Which one of the following choices is correct?
Correct Answer: D
A tautology is a formula which is “always true” . That is, it is true for every assignment of truth values to its simple components.
Method 1:
S1: (~p ^ (p Vq)) →q
The implication is false only for T->F condition.
Let’s consider q as false, then
(~p ^ (p Vq)) will be (~p ^ (p VF)) = (~p ^ (p)) =F.
It is always F->F which is true for implication. So there are no cases that return false, thus its always True i.e. its Tautology.
S2:
q->(~p (p Vq))
The false case for implication occurs at T->F case.
Let q=T then (~p (p Vq)) = (~p (p VT))= ~p. (It can be false for p=T).
So there is a case which yields T->F = F. Thus its not Valid or Not a Tautology.
Method 2:
