GATE DA 2025 Q15: Propositional logic: which statements are equivalent?

Let $p$ and $q$ be any two propositions. Consider the following propositional statements.

$S_1 : p \rightarrow q, \quad S_2 : \neg p \wedge q, \quad S_3 : \neg p \vee q, \quad S_4 : \neg p \vee \neg q,$

where $\wedge$ denotes conjunction (AND operation), $\vee$ denotes disjunction (OR operation), and $\neg$ denotes negation (NOT operation). Which one of the following options is correct? (Note: $\equiv$ denotes logical equivalence)