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