The logical statement $[ \sim \,( \sim \,P\, \vee \,q)\, \vee \,\left( {p\, \wedge \,r} \right)\, \wedge \,( \sim \,q\, \wedge \,r)]$ is equivalent to

$\sim p \wedge q$ is logically 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 the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.

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

$\sim (p \vee (\sim q))$ is equal to .......