- $(p \wedge q) \rightarrow r \\ \quad \Rightarrow \neg(p \wedge q) \vee r \\ \quad \Rightarrow \neg (p) \vee \neg (q) \vee r \\ \> \\ \left ( p \rightarrow r \right )\wedge \left ( q\rightarrow r \right ) \\ \quad \Rightarrow (\neg p \vee r) \wedge (\neg q \vee r) \\ \quad \Rightarrow \neg (p) \wedge \neg (q) \vee r \\ \quad \quad \textbf{they are not logically equivalent.} \\ \>$
- $\left ( \neg a\rightarrow b \right )\wedge \left ( \neg b\vee \left ( \neg a \vee \neg b \right )\right ) \\ \quad \Rightarrow (a \vee b) \wedge (\neg (a) \vee \neg(b)) \\ \quad \Rightarrow (a \wedge \neg a) \vee (a \wedge \neg b) \vee (\neg a \wedge b) \vee ( b \wedge \neg b) \\ \quad \Rightarrow (a \wedge \neg b) \vee (\neg a \wedge b) \\ \> \\ \neg \left ( a\leftrightarrow b \right ) \\ \quad \Rightarrow \neg ((a \rightarrow b) \wedge (b \rightarrow a)) \\ \quad \Rightarrow \neg ((\neg a \vee b) \wedge ( \neg b \vee a)) \\ \quad \Rightarrow (a \wedge \neg b) \vee (\neg a \wedge b) \\ \quad \quad \textbf{they are logically equivalent.} \\ \>$
$\text{ (i) is true, (ii) is false} \\ \textbf{B is correct.}$