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

If p : The total prime numbers between 2 to 100 are 26.

q : Zero is a complex number.

$r$ : Least common multiple (L.C.M.) of 6 and 7 is 6 .

Then which of the following is correct?