Among the statements:
$(S1)$ $\quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$
$(S2) \quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$
The negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to
For the statements $p$ and $q$, consider the following compound statements :
$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$
$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
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
$(\sim (\sim p)) \wedge q$ is equal to ………
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