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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Solution

The negation of the statement

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

is :

There exist real numbers a and b for which $a + b \neq b + a$ .

So, the given statement is not the negation of the first statement.

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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.

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