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, x²≠x.”

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