Question

Question 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.

Class X1 - Maths -Mathematical Reasoning Page 345

Answer 1

concept : negation of statement : if word 'not ' is not given in the statement , then insert word 'not ' in the statement . if word ' not ' is given in the statement then, remove word 'not ' from the statement .

(i) ~P : There exists at least one positive real number such that (x - 1) is not positive .

(ii)~q : All cats do not scratch.

(iii) ~r : There exists at least one real number such that neither x > 1 nor x < 1

(iv)~s : There does not exist a number such that 0 < x < 1