Class 11

Math

Algebra

Mathematical Reasoning

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 $x+y=y+x$

There exists real number $x$ and $y$ for which $x+y$ $=$ $y+x$. This is not the same as statement (ii).

Thus the given statements are not the negation of each other