The statement $\sim(p \leftrightarrow \sim q)$ is

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

Let $S$ be a non-empty subset of $\mathbb{R}$. Consider the following statement:

p : There is a rational number $x \in \mathrm{~S}$ such that $x>0$.

Which of the following statements is the negation of the statement p?

The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is