If the Boolean expression $( p \Rightarrow q ) \Leftrightarrow( q *(\sim p ))$ is a tautology, then the Boolean expression $p *(\sim q )$ is equivalent to

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

Which of the following is logically equivalent to $\sim(\sim p \Rightarrow q)$

The negation of the compound statement $^ \sim p \vee \left( {p \vee \left( {^ \sim q} \right)} \right)$ is

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 

Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p\Rightarrow (q\vee r)$ is