Are the following pairs of statements are negation of each other:
(i) The number x is not a rational number.
The number x is not an irrational number.
(ii) The number x is not a rational number.
The number x is an irrational number.

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Solution

(i) The number x is not a rational number.
The number x is not an irrational number.
The statements in this pair are the negation of each other.

(ii) The number x is not a rational number.
The number x is an irrational number.
The statements in this pair are not the negation of each other because both statements are the same. Both the statements convey that x is an irrational number.

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