Class 11 RD Sharma Solutions – Chapter 31 Derivatives – Exercise 31.4

**Question 1. Write the negation of each of the following statements:**

**(i) For every x ∈ N, x + 3 > 10**

**(ii) There exists x ∈ N, x + 3 = 10**

**Solution:**

(i)The negation of the statement is “There exist x ∈ N, such that x + 3 <= 10.”

(ii)The negation of the statement is “There exist x ∈ N, such that x + 3 ≠ 10.”

**Question 2. Negate each of the following statements:**

**(i) All the students complete their homework.**

**(ii) There exists a number which is equal to its square.**

**Solution:**

(i)Some of the students did not complete their homework.

(ii)For all real numbers x, x^{2}≠x.”