Negation of “Ram is in Class $X$ or Rashmi is in Class $XII$” is

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

Among the statements

$(S1)$: $(p \Rightarrow q) \vee((\sim p) \wedge q)$ is a tautology

$(S2)$: $(q \Rightarrow p) \Rightarrow((\sim p) \wedge q)$ is a contradiction

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

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

Negation of the Boolean statement $( p \vee q ) \Rightarrow((\sim r ) \vee p )$ is equivalent to