GATE CS 2021 Set 1 — Question 17
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Engineering Mathematics → Mathematical Logic → Propositional Logic
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Question
Let and be two propositions. Consider the following two formulae in propositional logic.Which one of the following choices is correct?
Correct answer
(B) S₁ is a tautology but S₂ is not a tautology.
Solution
Using distributive law: .
So is . Since is true only when is true, the implication is always true. Thus, is a tautology..
If is true and is true, then becomes . Thus, is not a tautology.
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