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.

Question

Philoid · Accepted Answer

The negation of first statement is

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

Which is not equal to second statement.

Hence given statement is false.

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.

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.