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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 $$x + y = y + x$$


Solution

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

Mathematics
NCERT
Standard XI

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