For the statements $p$ and $q$, consider the following compound statements :

$(a)$ $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$

$(b)$ $((p \vee q) \wedge \sim p) \rightarrow q$

Then which of the following statements is correct?

Negation of the Boolean expression $p \Leftrightarrow( q \Rightarrow p )$ is.

Which of the following Venn diagram corresponds to the statement “All mothers are women” ($M$ is the set of all mothers, $W$ is the set of all women)

Negation of the statement $(p \vee r) \Rightarrow(q \vee r)$ is :

$\sim p \wedge q$ is logically equivalent to

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.