Question

Check whether the following pair of statements is negation of each other. Give reasons for the answer
(i) $x+y=y+x$ is true for every real numbers $x$ and $y$
(ii) There exists real number $x$ and $y$ for which $x+y=y+x$

Answer 1

The negation of statement (i) is as follows
There exists real number $x$ and $y$ for which $x+y$ $\ne$ $y+x$. This is not the same as statement (ii).
Thus the given statements are not the negation of each other