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.


(i) The negation of the first statement is


The number x is a rational number.


Which is same as second statement


The number x is not an irrational number.


Hence the given pairs are negation of each other.


(ii) The negation of the first statement is


The number x is not a rational number.


Which is same as second statement


The number x is an irrational number.


Hence the given pairs are negation of each other.


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