Check whether the following pair of statements is negation of each other. Give reasons for the answer.

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 ≠ 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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