Write the negation of the following statement:
$s:$ All students study mathematics at the elementary level.

$(p \wedge \sim q) \wedge (\sim p \vee q)$ is :-

Let $p$ and $q$ be any two logical statements and $r: p \to (\sim p \vee q)$. If $r$ has a truth value $F$,then the truth values of $p$ and $q$ are respectively

For the simple statements $p, q$,and $r$,$p \rightarrow (q \vee r)$ is logically equivalent to

Which of the following statements 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.

What is the statement $(p$ $\rightarrow \sim p) \wedge (\sim p$ $\rightarrow p)$?