Propositional Logic GATE 2025 Question #10178 with Solution

GATE 2025 · session-5

AIPropositional LogicmediumMCQ1 mark

Let \( p \) and \( q \) be any two propositions. Consider the following propositional statements. S1: \( p \rightarrow q \), S2: \( \neg p \land q \), S3: \( \neg p \lor q \), S4: \( \neg p \lor \neg q \) where \( \land \) denotes conjunction (AND operation), \( \lor \) denotes disjunction (OR operation), and \( \neg \) denotes negation (NOT operation). (Note: \( \equiv \) denotes logical equivalence) Which one of the following options is correct?

A\( S_1 \equiv S_3 \)B\( S_2 \equiv S_3 \)C\( S_2 \equiv S_4 \)D\( S_1 \equiv S_4 \)

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