The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to
$(\sim x \wedge y) \vee(\sim x \wedge \sim y)$
$(x \wedge \sim y) \vee(\sim x \wedge y)$
$(x \wedge y) \vee(\sim x \wedge \sim y)$
$(x \wedge y) \wedge(\sim x \vee \sim y)$
The statement $(p \wedge(\sim q) \vee((\sim p) \wedge q) \vee((\sim p) \wedge(\sim q))$ is equivalent to
$\sim (p \vee q) \vee (\sim p \wedge q)$ is logically equivalent to
The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent to
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