Which of the following is true?

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
$I$: There exists real numbers $x$ and $y$ for which $x+y=y+x.$
$II$: For all real numbers $x$ and $y$,$x+y \neq y+x.$

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

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 statements are true and which are false? In each case give a valid reason for saying so.
$s:$ If $x$ and $y$ are integers such that $x > y,$ then $-x < -y.$

Write the negation of the following statement:
$s:$ All students study mathematics at the elementary level.