$\begin{array}{1 1} yes \\ no \end{array} $

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The given statements are:

$p: x+y=y+x$ is true for every real number $x\:\:and\:\:y$.

$q:$ There exists real numbers $x\:\:and\:\:y$ for which $x+y=y+x$

Negation of $p$ is

$x+y=y+x$ is not true for every real number $x\:\:and\:\:y$

That is $x+y\neq y+x$ for every real number $x\:\:and\:\:y$

But this is not the statement $q$.

$\therefore$ Both the statements $p\:\:and\:\:q$ are not the negation of each other.

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