The proposition $p \Rightarrow \;\sim (p\; \wedge \sim \,q)$ is

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

If $(p \wedge \sim q) \wedge r  \to \sim r$ is $F$ then truth value of $'r'$ is :-

Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

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

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.