The negation of the Boolean expression $((\sim q) \wedge p) \Rightarrow((\sim p) \vee q)$ is logically equivalent to
$p \Rightarrow q$
$q \Rightarrow p$
$\sim(p \Rightarrow q)$
$\sim(q \Rightarrow p)$
$\left(p^{\wedge} r\right) \Leftrightarrow\left(p^{\wedge}(\sim q)\right)$ is equivalent to $(\sim p)$ when $r$ is.
If $p$ and $q$ are simple propositions, then $p \Leftrightarrow \sim \,q$ is true when
The logical statement $[ \sim \,( \sim \,P\, \vee \,q)\, \vee \,\left( {p\, \wedge \,r} \right)\, \wedge \,( \sim \,q\, \wedge \,r)]$ 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
$p \Rightarrow q$ can also be written as