# Identify the quantifier in the following statements and write the negation of the statements

(i) There exists a number which is equal to its square

(ii) For every real number x, x is less than x + 1

(iii) There exists a capital for every state in India

**Solution:**

The negation of a statement is a statement that gives the opposite meaning of the given statement.

**(i)** The quantifier is ‘There exists’.

The negation of this statement is as follows.

There does not exist a number which is equal to its square.

**(ii)** The quantifier is ‘For every’.

The negation of this statement is as follows.

There exists a real number x, such that x is not less than x + 1.

**(iii)** The quantifier is ‘There exists’.

The negation of this statement is as follows.

There exists a state in India which does not have a capital

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.3 Question 2

## Identify the quantifier in the following statements and write the negation of the statements. (i) There exists a number which is equal to its square. (ii) For every real number x, x is less than x + 1. (iii) There exists a capital for every state in India.

**Summary:**

(i) The quantifier is ‘There exists’ and the negation of the statement is there does not exist a number which is equal to its square

(ii) The quantifier is ‘For every’ and the negation is there exist a real number x , such that x is not less than x + 1

(iii) The quantifier is ‘There exists’ and the negation is there exists a state in India which does not have a capital