Given the following two statements :

$\left( S _{1}\right):( q \vee p ) \rightarrow( p \leftrightarrow \sim q )$ is a tautology.

$\left( S _{2}\right): \sim q \wedge(\sim p \leftrightarrow q )$ is a fallacy.

Then

Among the statements:

$(S1)$ $\quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$

$(S2) \quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$

Which of the following  statements is $NOT$  logically equivalent to $\left( {p \to  \sim p} \right) \to \left( {p \to q} \right)$?

Let $p$ and $q$ be any two logical statements and $r:p \to \left( { \sim p \vee q} \right)$. If $r$ has a truth value $F$, then the truth values of $p$ and $q$ are respectively

If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively

Which of the following is an open statement