The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:

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 statement : - $\sqrt{5}$ is an integer or $5$ is irrational is

Statement$-I :$  $\sim (p\leftrightarrow q)$ is equivalent to $(p\wedge \sim  q)\vee \sim  (p\vee \sim  q) .$
Statement$-II :$  $p\rightarrow (p\rightarrow q)$ is a tautology.

Negation of “Ram is in Class $X$ or Rashmi is in Class $XII$” is

The Boolean expression $ \sim \left( {p \Rightarrow \left( { \sim q} \right)} \right)$ is equivalent to