The Boolean expression $((p \wedge q) \vee (p \vee \sim q)) \wedge (\sim p \wedge \sim q)$ is equivalent to

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

Which of the following logical statements is a tautology?

Let $p$ and $q$ be two statements. Then $\sim(p \wedge (p \Rightarrow \sim q))$ is equivalent to:

Consider the following statements:
$P :$ Suman is brilliant
$Q :$ Suman is rich
$R :$ Suman is honest
The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as:

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