The negation of the statement $q \wedge \left( { \sim p \vee  \sim r} \right)$

Consider the following three statements :

$(A)$ If $3+3=7$ then $4+3=8$.

$(B)$ If $5+3=8$ then earth is flat.

$(C)$ If both $(A)$ and $(B)$ are true then $5+6=17$. Then, which of the following statements is correct?

If the Boolean expression $\left( {p \oplus q} \right) \wedge \left( { \sim p\,\Theta\, q} \right)$ is equivalent to $p \wedge q$, where $ \oplus $ , $\Theta  \in \left\{ { \wedge , \vee } \right\}$ , ,then the ordered pair $\left( { \oplus ,\Theta } \right)$ is 

If $p$ : It rains today, $q$ : I go to school, $r$ : I shall meet any friends and $s$ : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.

The logically equivalent of $p \Leftrightarrow q$ is :-

The negative of the statement $\sim p \wedge(p \vee q)$ is