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.

Solution:

(i) The first statement is  'The number x is not a rational number'.

Its negation is ‘the number x is a rational number’.

It is same as the second statement. This is because if a number is a rational number only if is not an irrational number.

Thus, the given pairs of statements are negations of each other.

(ii) The first statement is 'The number x is a rational number'.

Its negation is ‘the number x is not a rational number’.

This means that the number x is irrational, which is the same as the second statement.

Thus, the given pairs of statements are negations of each other

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.2 Question 2

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

Summary:

(i) The given pairs of statements are negations of each other. (ii) The given pairs of statements are negations of each other