The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

The statement pattern $(p \lor q) \to \sim r$ is logically equivalent to

The negation of the inverse of the statement $\sim p \lor q$ 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 $p$: switch $S_1$ is closed,$q$: switch $S_2$ is closed,$r$: switch $S_3$ is closed,then the symbolic form of the following switching circuit is equivalent to:

Which of the following sentences are statements? Give reasons for your answer.
Mathematics is difficult.