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

$\sim ((\sim p)\; \wedge q)$ is equal to

If $p , q$ and $r$ are three propositions, then which of the following combination of truth values of $p , q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?

If the Boolean expression $\left( {p \oplus q} \right) \wedge \left( { \sim p\,\Theta\, q} \right)$ is equivalent to $p \wedge q$, where $ \oplus $ , $\Theta  \in \left\{ { \wedge , \vee } \right\}$ , ,then the ordered pair $\left( { \oplus ,\Theta } \right)$ is 

The expression $ \sim ( \sim p\, \to \,q)$ is logically equivalent to