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.

Asked by Pragya Singh | 11 months ago |  89

1 Answer

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 for which 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 whose capital does not exists.

Answered by Abhisek | 11 months ago

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