RBSE Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Textbook Exercise Questions and Answers.

RBSE Class 11 Maths Solutions Chapter 14 Mathematical Reasoning Ex 14.2

Question 1.
Write the negation of the following statements:
(i) Chennai is the capital of Tamil Nadu.
(ii) 4l 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) The negation of the statement is Chennai is not the capital of Tamil Nadu.
(ii) The negation of the statement is :
√2 is a complex number.
(iii) The negation of the statement is :
All the triangles are equilateral triangles.
(iv) The negation of the statement is :
Number 2 is not more than number 7.
(v) The negation of the statement is : .
Each 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) First statement p: number x is not a rational number its negation q: number x is a rational number or number x is not an irrational number.
Second statement r: number x is not a irrational number. Thus, two statements are negation of each others.

(ii) First statement
p: number x is a rational number its negation
q : number x is not a rational number. i.e., number x is an irrational number.
Second statement r: number* is an irrational number.
Thus, two statements are negation to 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) Number 3 is prime or odd.
Given statement: Number 3 is prime or odd First component statement p: number 3 is prime.
Second component statement q: number 3 is odd Here, both component statement are true.
Thus, given statement is true.

(ii) All the integers are positive or negative.
Given statement: All integers are positive or negative.
First component statement p: All integers are positive. Second component statement q: All integers are negative. Since, component statement p and q both are false.
Thus, given statement is false.

(iii) Number 100 is divisible by 3, 11 and 5.
Given statement: Number 100 is divisible by 3,11 and 5 First component statement p: number 100 is divisible by 3. (which is false)
Second component statement q: number 100 is divisible by 11 (which is false)
Third component statement r: number 100 is divisible by number 5 (which is true)
Here, component statements p, q are false and component statement r is true.
Thus, given statement is false.