The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee  \sim \left( {p\, \vee q} \right)$ is logically equivalent to

Consider the two statements :

$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology

$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.

Then :

Which Venn diagram represent the truth of the statement“Some teenagers are not dreamers”

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to 

The negation of the statement $q \wedge \left( { \sim p \vee  \sim r} \right)$