The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to

$( S 1)( p \Rightarrow q ) \vee( p \wedge(\sim q ))$ is a tautology $( S 2)((\sim p ) \Rightarrow(\sim q )) \wedge((\sim p ) \vee q )$ is a Contradiction. Then

Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(\sim p) \Rightarrow(p \wedge q) \vee r \quad$ is a tautology. Then ' $r$ ' is equal to

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to 

The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to

Let $p$ and $q$ be two Statements. Amongst the following, the Statement that is equivalent to $p \to q$ is