The negation of the statement "If $5 < 7$ and $7 > 2$,then $5 > 2$" is

Write the negation of the following statement:
$q:$ There exists a rational number $x$ such that $x^{2} = 2$.

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:

Which of the following is not a correct statement?

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

The statement $(p$ $\rightarrow (q$ $\rightarrow p))$ $\rightarrow (p$ $\rightarrow (p \vee q))$ is