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

$$ \begin{aligned} & S_1: p \rightarrow q, \quad S_2: \neg p \wedge q, \quad S_3: \neg p \vee q, \\ & S_4: \neg p \vee \neg q, \end{aligned} $$

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)