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

(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 exist 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.