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 negation of statement (i) is as follows.

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.

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Similar questions

Check whether the following pair of statements are negations 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.

x + y = y + x

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x + y = y + x

x + y = y + x

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Check whether the following pair of statements are negation of each other. Give reason for your answer.

(i) a+b = b + a is true for every real number a and b.

(ii) There exists real numbers a and b for which a+b = b + a.

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