Negation of the Boolean statement $(p \vee q) \Rightarrow ((\sim r) \vee p)$ 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 equivalently expressed as:

Which of the following statements is a tautology?

The negation of the Boolean expression $\sim s \vee (\sim r \wedge s)$ is equivalent to

Given the following two statements:
$(S_{1}): (q \vee p) \rightarrow (p \leftrightarrow \sim q)$ is a tautology.
$(S_{2}): \sim q \wedge (\sim p \leftrightarrow q)$ is a fallacy.
Then:

The statement $[(p$ $\rightarrow q) \wedge \sim q]$ $\rightarrow r$ is a tautology,when $r$ is equivalent to