The logical statement $(p$ $\rightarrow q) \wedge (p$ $\rightarrow \sim p)$ is equivalent to

Consider the following statements:
$p$: the switch $S_1$ is closed.
$q$: the switch $S_2$ is closed.
$r$: the switch $S_3$ is closed.
Then the switching circuit represented by the statement $(p \wedge q) \vee (\sim p \wedge (\sim q \vee p \vee r))$ 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.

Find the component statements of the following compound statement:
The sky is blue and the grass is green.

Negation of the Boolean expression $p \Leftrightarrow (q \Rightarrow p)$ is:

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