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.

Question

Philoid · Accepted Answer

(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.

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.