Are the following pairs of statements are a negation 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 not a rational number.
The number x is an irrational number.
(i) The number x is not a rational number.
= The number x is an irrational number.
Since The statement “The number x is not a rational number.” is a negation of the first statement.
(ii) The number x is not a rational number.
= The number x is an irrational number.
Since The statement “The number x is a rational number.” Is not a negation of the first statement.