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 .

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Solution

The contradiction of a statement is called the negation of a statement.

(i) The given statement is: x+y=y+x is true for every real numbers x and y. The negation of the given statement is x+y=y+x is not true for every real numbers x and y.

(ii) The given statement is: there exists real numbers x and y for which x+y=y+x .

Since the statement (ii) is same as statement (i) but it is not the negation of the statement (i) neither statement (i) is negation of statement (ii), thus it can be said that both statements are not the negation of each other.

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