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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


Solution

(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

Mathematics
NCERT
Standard XI

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