MENU

RD Chapter 31 Mathematical Reasoning Ex 31.4 Solutions

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.”

Free - Previous Years Question Papers
Any questions? Ask us!
×