Question

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.

Class X1 - Maths -Mathematical Reasoning Page 335

Answer 1

concept : Quantifiers are ' there exists ' and ' for every ' .

(i) Quantifier :- There exists
P : There exists a number which is equal to its square .
not P ( ~P) : There does not exist a number which is equal to its square.

(ii) Quantifier :- For every
P : For every real number x , x is less than (x +1)
not P(~P) : There exists a real number x such that x is not less than ( x + 1).

(iii) Quantifier :- There exists
P : There exists a capital for every state of India .
not P (~P) : There does not exist a capital for every state of India .