Negate each of the following statements :

(i) All the students completed their homework.

(ii) There exists a number which is equal to its square.

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Solution

(i) The negation of the statement

All the students completed their homework.

is

Some of the students did not complete their home work.

(ii) The negation of the statement

There exists a number which is equal to its square.

is

For every resl number $x, x^{2} \neq x$

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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 statement:

'There does not exist a quadrilateral which has all its sides equal'

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