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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
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The negation of statement (i) is as follows
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

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