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.
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.

Answers:

(i)

“The number x is an irrational number.”

The statement “The number x is not a rational number.”

It is a negation of the first statement.

(ii)

“The number x is an irrational number.”

The statement “The number x is a rational number.”

It is not a negation of the first statement.