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

p: $x + y = y + x$ is true for every real numbers $x$ and $y$.
q: There exists real numbers $x$ and $y$ for which $x + y = y + x$.

The negation of p is:

There exists no real numbers x and y for which $x + y = y + x$

which is not equal to q.

Hence the given pair of statements are not negation of each other.

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