Check whether the following pair of statements is a negation of each o

1.	Check whether the following pair of statements is a 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.
Answer» The negation of statement is as follows. (i) 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.

Check whether the following pair of statements is a 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.

Answer»

The negation of statement is as follows.

(i) 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.