The negative of $q\; \vee \sim (p \wedge r)$ is

The statement $(\mathrm{p} \wedge(\mathrm{p} \rightarrow \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r})) \rightarrow \mathrm{r}$ is :

The negation of the compound statement $^ \sim p \vee \left( {p \vee \left( {^ \sim q} \right)} \right)$ is

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

Given the following two statements :

$\left( S _{1}\right):( q \vee p ) \rightarrow( p \leftrightarrow \sim q )$ is a tautology.

$\left( S _{2}\right): \sim q \wedge(\sim p \leftrightarrow q )$ is a fallacy.

Then

The contrapositive of $(p \vee q) \Rightarrow r$ is