# 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