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

Let $F_{1}(A, B, C)=(A \wedge \sim B) \vee[\sim C \wedge(A \vee B)] \vee \sim A$ and $F _{2}( A , B )=( A \vee B ) \vee( B \rightarrow \sim A )$ be two logical expressions. Then ...... .

$\left( { \sim \left( {p \vee q} \right)} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to 

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

Statement $-1$ : The statement $A \to (B \to A)$ is equivalent to $A \to \left( {A \vee B} \right)$.

Statement $-2$ : The statement $ \sim \left[ {\left( {A \wedge B} \right) \to \left( { \sim A \vee B} \right)} \right]$ is a Tautology