What is the dual statement of the statement "Rina is healthy and Mina is beautiful"?

If the truth value of the compound statement $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is $False$, then the truth values of $p \to q$ and $q \to p$ are respectively......

Rewrite the following statement in the form "$p$ if and only if $q$":
For you to get an $A$ grade,it is necessary and sufficient that you do all the homework regularly.

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:
$p$ : There is a rational number $x \in S$ such that $x > 0$.
Which of the following statements is the negation of the statement $p$?

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.

Consider
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.