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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.



Answer -

(i) The quantifier is тАЬThere existsтАЭ.
The negation of this statement is as follows.
There does not exist a number which is equal to its square.
(ii) The quantifier is тАЬFor everyтАЭ.
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 тАЬThere existsтАЭ.
The negation of this statement is as follows.
There exists a state in India which does not have a capital.

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