NCERT Class XI Mathematics - Mathematical Reasoning - Solutions
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Question : 7
Total: 25
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.
(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) Here the quantifier is ‘there exists’.
The negation of statement is : There does not exist a number which is equal to its square.
(ii) Here the quantifier is ‘for every’
The negation of statement is : For atleast 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.
The negation of statement is : There does not exist a number which is equal to its square.
(ii) Here the quantifier is ‘for every’
The negation of statement is : For atleast 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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