Let $r \in\{p, q, \sim p, \sim q\}$ be such that the logical statement $r \vee(\sim p) \Rightarrow(p \wedge q) \vee r \quad$ is a tautology. Then ' $r$ ' is equal to

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

The statement $p \rightarrow  (q \rightarrow p)$  is equivalent to

Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$

Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.

The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to

Which Venn diagram represent the truth of the statements “No child is naughty”

Where $U$ = Universal set of human beings, $C$ = Set of children, $N$ = Set of naughty persons