## NCERT Solutions for Class 11 Maths Chapter 14 – Mathematical Reasoning Ex 14.2

#### Page No 329:

#### Question 1:

Write the negation of the following statements:

(i) Chennai is the capital of Tamil Nadu.

(ii) is not a complex number.

(iii) All triangles are not equilateral triangle.

(iv) The number 2 is greater than 7.

(v) Every natural number is an integer.

#### Answer:

(i) Chennai is not the capital of Tamil Nadu.

(ii) is a complex number.

(iii) All triangles are equilateral triangles.

(iv) The number 2 is not greater than 7.

(v) Every natural number is not an integer.

#### Question 2:

Are the following pairs of statements negations of each other?

(i) The number

*x*is not a rational number.
The number

*x*is not an irrational number.
(ii) The number

*x*is a rational number.
The number

*x*is an irrational number.#### Answer:

(i) The negation of the first statement is “the number

*x*is a rational number”.
This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number.

Therefore, the given statements are negations of each other.

(ii) The negation of the first statement is “the number

*x*is not a rational number”. This means that the number*x*is an irrational number, which is the same as the second statement.
Therefore, the given statements are negations of each other.

#### Question 3:

Find the component statements of the following compound statements and check whether they are true or false.

(i) Number 3 is prime or it is odd.

(ii) All integers are positive or negative.

(iii) 100 is divisible by 3, 11 and 5.

#### Answer:

(i) The component statements are as follows.

*p*: Number 3 is prime.

*q*: Number 3 is odd.

Both the statements are true.

(ii) The component statements are as follows.

*p*: All integers are positive.

*q*: All integers are negative.

Both the statements are false.

(iii) The component statements are as follows.

*p*: 100 is divisible by 3.

*q*: 100 is divisible by 11.

*r*: 100 is divisible by 5.

Here, the statements,

*p*and*q*, are false and statement*r*is true._{}

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