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.

Question

Philoid · Accepted Answer

(i) Quantifier is 'There exists'.

Negation of statement is

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

(ii) Quantifier is 'For Every'.

Negation of statement is

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

(iii) Quantifier is 'There exists'.

Negation of statement is

There does not exist a capital for every state in India.

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.