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Complex Numbers

Check whether...

Question

Check whether the following pair of statements are negation of each other. Give reasons for your answer.
(i) a + b = b + a is true for every real number a and b.
(ii) There exist real numbers a and b for which a + b = b + a.

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Solution

The given statements are not negation of each other because the negation of " $a + b = b + a$ is true for every real number a and b" is "There exist real numbers a and b for which $a + b \neq b + a$ ".

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Check whether the following pair of statements are negations of each other. Give reasons for your answer.

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