Let p and q be two propositions. Consider the following two formulae in propositional logic. S 1 : (¬p ∧ (p ∨ q)) → q S 2 : q → (¬p ∧ (p ∨ q)) Which one of the following choices is correct?

Correct Answer is : S1 is a tautology but S2 is not a tautology.

Neither S 1 nor S 2 is a tautology.

S 1 is not a tautology but S 2 is a tautology.

Both S 1 and S 2 are tautologies.

S 1 is a tautology but S 2 is not a tautology.

GATE Computer Science (CS) 2021 Shift 1 Solved Paper

Question : 17 of 65

Marks: +1, -0

Let p and q be two propositions. Consider the following two formulae in propositional logic.
S₁ : (¬p ∧ (p ∨ q)) → q
S₂ : q → (¬p ∧ (p ∨ q))
Which one of the following choices is correct?

Neither S₁ nor S₂ is a tautology.
S₁ is not a tautology but S₂ is a tautology.
Both S₁ and S₂ are tautologies.
S₁ is a tautology but S₂ is not a tautology.

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