Question

(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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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

Therefore the given statements are negations of each other

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