Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 11 Maths Chapter 14 Mathematical Reasoning Ex 14.2
Question 1.
Write the negation of the following statements:
- Chennai is the capital of Tamil Nadu.
- \(\sqrt{2}\) is not a complex number.
- All triangles are not equilateral.
- The number 2 is greater than 7.
- Every natural number is an integer.
Solution:
Negation of the given statements are:
- Chennai is not the capital of Tamil Nadu.
- \(\sqrt{2}\) is a complex number.
- All triangles are equilateral.
- The number 2 is not greater than, 7.
- Every natural number is not an integer.
Question 2.
Are the following pair of statements negation of each other?
(а) The number x is not a rational number.
The number x is not an irrational number.
(b) The number x is a rational number.
The number x is an irrational number.
Solution:
(a) The negation of the statement:
“The number x is not a rational number” is
The number x is a rational number.
The second statement is the same x is not irrational. Therefore, those statement are negation of each other.
(b) The negation of the statement is The number x is a rational number.
The number x is not a rational number or we can say x is irrational number. The second statement is the same. Therefore, they are negations of each other.
Question 3.
Find the component statements of the following compound statements and check whether they are true or false:
- The number 3 is prime or it is odd.
- All integers are positive or negative.
- 100 is divisible by 3, 11 and 5.
Solution:
1. p : The number 3 is prime.
q : The number 3 is odd.
p, q are connected by or It is true.
2. p : All integers are positive.
q : All integers are negative.
p, q are connected by the word or. p and q both are false.
So, it is false.
3. p : 100 is divisible by 3.
q : 100 is divisible by 11.
q : 100 is divisible by 5.
p is false, q is false, r is true.
p and q and r is a false statement.