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Question
Check whether the following pair of statements are negation of each other. Give reasons for your answer.
a + b = b + a is true for every real number a and b.
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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