Question

Are the following pairs of statements negations of each other?
(i) The number is not a rational number
The number is not an irrational number
(ii) The number is a rational number
The number is an irrational number

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Solution
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(i) Let the number is not a rational number
The negation of is "the number 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 the number is a rational number
The negation of the first statement is "the number is not a rational number" .
This means that the number is an irrational number which is the same as the second statement
Therefore the given statements are negations of each other

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Mathematics
NCERT
Exercise 14.2
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