Question

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.

Answer 1

Answer:

Step-by-step explanation:

Here, the quantifier is ‘there exists’.

The negation of this statement is as follows

There does not exists a number which is equal to its square

(ii) Here, the quantifier is ‘for every’.

The negation of this statement is as follows

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

(iii) Here, the quantifier is ‘there exists’.

The negation of this statement is as follows

In India there exists a state, which does not have a capital.