The logically equivalent proposition of $p \Leftrightarrow q$ is

The proposition $p \Rightarrow \sim (p \wedge \sim q)$ is

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 ...... .

The logical statement $(p \lor q) \land [(\sim p \land q) \lor (p \land \sim q)] \land \sim q$ is logically equivalent to ...

The negation of $p \wedge (q \rightarrow r)$ is

Which of the following statement$(s)$ is/are not true?
$I$) If $1$ is not a prime number, then $2$ is not a prime number.
$II$) $e$ is a vowel and $12 \times 3 = 36$.
$III$) It is not true that $14$ is a composite number and $3$ is an even number.
$IV$) $\sqrt{5}$ is an irrational number, but $3 + \sqrt{5}$ is a complex number.