Negation of the statement : - $\sqrt{5}$ is an integer or $5$ is irrational is

The expression $ \sim ( \sim p\, \to \,q)$ is logically equivalent to

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

Let $p$ and $q$ denote the following statements
$p$ : The sun is shining
$q$ : I shall play tennis in the afternoon

The negation of the statement "If the sun is shining then I shall play tennis in the afternoon", is 

The statement $A \rightarrow( B \rightarrow A )$ is equivalent to

Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then