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
Solution:
The negation of a statement is a statement that gives the opposite meaning of the given statement.
(i) The quantifier is ‘There exists’.
The negation of this statement is as follows.
There does not exist a number that is equal to its square.
(ii) The quantifier is ‘For every’.
The negation of this statement is as follows.
There exists a real number x, such that 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 which does not have a capital
NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.3 Question 2
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.
Summary:
(i) The quantifier is ‘There exists’ and the negation of the statement is there does not exist a number which is equal to its square
(ii) The quantifier is ‘For every’ and the negation is there exist a real number x , such that x is not less than x + 1
(iii) The quantifier is ‘There exists’ and the negation is there exists a state in India which does not have a capital
visual curriculum