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.

Solution:

The negation of a statement should give exactly the opposite meaning of the statement. i.e., if the given statement is true then its negation must be false, and vice versa. Accordingly,

(i) The negation of statement p is as follows:

There exists a positive real number x such that x - 1 is not positive.

(ii) The negation of statement q is as follows:

There exists a cat that does not scratch.

(iii) The negation of statement r is as follows:

There exists a real number x such that neither x > 1 nor x < 1.

(iv) The negation of statement s is as follows:

There does not exist any number x such that 0 < x < 1

NCERT Solutions Class 11 Maths Chapter 14 Exercise ME 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

Summary:

The negations of the following statements are (i) There exists a positive real number x such that x - 1 is not positive. (ii) There exists a cat that does not scratch. (iii) There exists a real number x such that neither x > 1 nor x < 1. (iv) There does not exist a number x such that 0 < x < 1