Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is

$\sim ((\sim p)\; \wedge q)$ is equal to

Negation of the compound proposition : If the examination is difficult, then I shall pass if I study hard

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 

Consider the following statements 

$P :$ Suman is brilliant

$Q :$ Suman is rich

$R :$ Suman is honest

The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as 

Given the following two statements :

$\left( S _{1}\right):( q \vee p ) \rightarrow( p \leftrightarrow \sim q )$ is a tautology.

$\left( S _{2}\right): \sim q \wedge(\sim p \leftrightarrow q )$ is a fallacy.

Then