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.

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Solution

(i) Here the quantifier is 'there exists'.

The negation of statement is: There exists a number which is not equal to its square.

(ii) Here the quantifier is 'for every'.

The negation of statement is: For at least one real number x, x is not less than x + 1.

(iii) Here the quantifier is 'there exists'.

The negation of statement is: There exists a state in India which does not have a capital.

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Similar questions

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.

x, x

x + 1

Write the negation of the following statements:

(i) p: For every positive real number x, the number x – 1 is also positive.

(ii) q: All cats scratch.

(iii) r: For every real number x, either x > 1 or x < 1.

(iv) s: There exists a number x such that 0 < x < 1.

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