# PSEB 11th Class Maths Solutions Chapter 14 Mathematical Reasoning Ex 14.2

Punjab State Board PSEB 11th Class Maths Book Solutions Chapter 14 Mathematical Reasoning Ex 14.2 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 11 Maths 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) √2 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.
The negation of the given statements is as follows:
(i) Chennai is not the capital of Tamil Nadu.
(ii) √2 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.
(i) The negation of the first statement:
The number x is “a rational number”.
Which is the same as the second statement.
This is because when a number is statement not rational, it is rational.
Therefore, given statements are negation of each other.

(ii) The negation of the first statement:
The number x is an irrational number.
The second statement, which is the same as the second statement.
Therefore they are negation 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.
(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.