Check whether the following pair of statements are 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 numbers x and y for which x + y = y + x.

Solution:

The negation of statement (i) is as follows:

"There exists real numbers x and y for which x + y ≠ y + x". This is not the same as the statement (ii)

Thus, the given statements are not negations of each other

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.3 Question 3

Check whether the following pair of statements are 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 numbers x and y for which x + y = y + x

Summary:

The given statements are not negations of each other