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.