Question 15316 – DSSSB PGT 2021
March 21, 2024UGC NET CS 2013 Dec-paper-2
March 21, 2024Propositional-Logic
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Question 1
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Which one of the following choices is correct?
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Both S1and S2 are tautologies.
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Neither S1and S2 are tautology.
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S1is not a tautology but S2is a tautology.
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S1is a tautology but S2is not a tautology.
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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:
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: