3.    Check whether the following pair of statements are negation of each other. Give reasons for your 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.

Answers (1)

p: x + y = y + x is true for every real numbers x and y.
q: There exists real numbers x and y for which x + y = y + x.

The negation of p is:

There exists no real numbers x and y for which x + y = y + x

which is not equal to q.

Hence the given pair of statements are not negation of each other.

Exams
Articles
Questions