Class 11 NCERT Solutions – Chapter 14 Mathematical Reasoning – Exercise 14.2

Question 1. Write the negation of the following statements:

(i) Chennai is the capital of Tamil Nadu.

The negation of the statement is 

Chennai is not the capital of Tamil Nadu.

Or

It is false that chennai is the capital of Tamil Nadu.

(ii) √2 is not a complex number

The negation of the statement is 

√2 is a complex number

Or

It is false that √2 is not a complex number

(iii) All triangles are not equilateral triangle.

The negation of the statement is

All triangles are equilateral triangle.

Or

It is false that all triangles are not equilateral triangle.

(iv) The number 2 is greater than 7.

The negation of the statement is

 The number 2 is not greater than 7.

Or

It is false that the number 2 is greater than 7.

(v) Every natural number is an integer.

The negation of the statement is

 Every natural number is not an integer.

Or

It is false that every natural number is 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.

Yes, they both are the negation of each other because negation of first statement  is 

The number x is a rational number.

which means that x is not an irrational number so the negation can also be written as 

The number x is not an irrational number

Note: There are two types of number rational number and irrational number. If a number is not rational it will be irrational and vice-versa.

(ii) The number x is a rational number.

The number x is an irrational number.

Yes, they both are the negation of each other because the negation of the first statement  is

The number x is not a rational number.

which means that x is an irrational number so the negation can also be written as

The number x is an irrational number

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.

The component statements are 

p: Number 3 is prime

q: Number 3 is odd

Here the connecting word is or therefore we know that if anyone the statement is true than whole statement will be true.

We know that 3 is both prime as well as odd number

p -> TRUE

q -> TRUE

Hence, the statement is TRUE.

(ii) All integers are positive or negative.

The component statements are

p: All integers are positive

q: All integers are negative

Here the connecting word is Or therefore we know that the statement will only be FALSE if both statement are false.

we also know that 0 is neither positive nor negative.

p -> FALSE

q -> FALSE

Hence, the statement is FALSE.

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

The component statements are

p: 100 is divisible by 3

q: 100 is divisible by 11

r: 100 is divisible by 5

Here the connecting word is AND therefore we know that the statement will be FALSE if any of the statement is false.

we also know that 100 is not divisible by 3 and 11 but it is divisible by 5.

p -> FALSE

q -> FALSE

r -> TRUE

Hence, the statement is FALSE.