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

The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :

$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.

Which Venn diagram represent the truth of the statement“All students are hard working.”

Where $U$ = Universal set of human being, $S$ = Set of all students, $H$ = Set of all hard workers.

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

The statement $(p \Rightarrow q) \vee(p \Rightarrow r)$ is NOT equivalent to.