Question

Identify the quantifier in the following statements and write the negation of the statement. 

(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

(i) Quantifier is‘there exists’ 

The negation is, 

There doesn’t exist a number which is equal to its square. 

(ii) Quantifier is ‘For every’ 

The negation is, there exist a real number x such that x is not less than x + 1 

(iii) Quantifier is ‘there exists’ 

The negation state in India which doesn’t have a capital