If $(p\; \wedge \sim r) \Rightarrow (q \vee r)$ is false and $q$ and $r$ are both false, then $p$ is

Which one of the following is a tautology ?

$\sim (p \wedge q)$ is equal to …..

Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$

Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.

Let $p , q , r$ be three logical statements. Consider the compound statements $S _{1}:((\sim p ) \vee q ) \vee((\sim p ) \vee r ) \text { and }$ and $S _{2}: p \rightarrow( q \vee r )$ Then, which of the following is NOT true$?$