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RD Chapter 31- Mathematical Reasoning Ex-31.4 Interview Questions Answers

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

Answer 1 :

(i) For every x ∈ N, x + 3 > 10
The negation of the statement is
“There exist x ∈ N, such that x + 3 ≥ 10.”
(ii) There exists x ∈ N, x + 3 = 10
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.

Answer 2 :

(i) All the students complete their homework.
The negation of the statement is
“Some of the students did not complete their homework.”
(ii) There exists a number which is equal to its square.
The negation of the statement is
“For every real number x, x2≠x.”


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