If $\sim p \to q$ is false and $q \leftrightarrow r$ is false, then the truth value of $(p, q, r)$ is...

If $p \to (q \lor \sim r)$ is false, then the truth values of $(p \leftrightarrow q) \land r$ and $\sim p \to \sim q$ are :

The contrapositive of the statement "If $x \in A$ or $x \in B$,then $x \in A \cup B$" 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.

If $\sim p \lor q$ is false, then which of the following is correct?

Statement $-1$: The statement $A \to (B \to A)$ is equivalent to $A \to (A \vee B)$.
Statement $-2$: The statement $\sim [(A \wedge B) \to (\sim A \vee B)]$ is a tautology.