Are the following pairs of statements negations 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 a rational number. The number x is an irrational number.
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(i) Let p: the number x is not a rational number
The negation of p is "the number x is a rational number"
This is same as the second statement as if a number is not an irrational number then it is a rational number
Therefore the given statements are negations of each other
(ii) Let p: the number x is a rational number
The negation of the first statement is "the number x is not a rational number" .
This means that the number x is an irrational number which is the same as the second statement
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