Among the statements:
$(S1): (p \Rightarrow q) \vee ((\sim p) \wedge q)$ is a tautology
$(S2): (q \Rightarrow p) \Rightarrow ((\sim p) \wedge q)$ is a contradiction

If $p$ and $q$ are true statements and $r$ is a false statement,then which of the following is correct?

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.

Write the negation of the following statement:
$p:$ For every real number $x, x^{2} > x.$

The compound statement $p \wedge (\sim p \wedge q)$ is

Write the negation of the following statement:
$r:$ For every real number $x$,either $x > 1$ or $x < 1.$