## myCBSEguide App

CBSE, NCERT, JEE Main, NEET-UG, NDA, Exam Papers, Question Bank, NCERT Solutions, Exemplars, Revision Notes, Free Videos, MCQ Tests & more.

Install Now

**Exercise 14.2**

**1. Write the negation of the following statements:**

**(i) Chennai is the capital of Tamilnadu.**

**(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.**

**Ans. (i) **Negation of statement is: Chennai is not the capital of Tamilnadu.

**(ii) **Negation of statement is: is a complex number.

**(iii) **Negation of statement is: All triangles are equilateral triangle.

**(iv) **Negation of statement is: The number 2 is not greater than 7.

**(v) **Negation of statement is: Every natural number is not an integer.

**2. Are the following pairs of statements negations of each other:**

**(i) The number **** is not a rational number.**

**The number is not an irrational number**

**(ii) The number **** is a rational number.**

**The number is an irrational number**

**Ans. (i) **Let The number is not a rational number.

The number is not an irrational number.

Now The number is a rational number.

And The number is an irrational number.

and

Therefore, and are negation of each other.

**(ii) **Let The number is a rational number.

The number is an irrational number.

Now The number is not a rational number.

And The number is not an irrational number.

and

Therefore, and are negation of each other.

**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.**

**Ans. (i) **The component statements are:

Number 3 is prime number.

It is an odd number.

Both the component statements and are true.

**(ii) **The component statements are:

All integers are positive.

All integers are negative.

Both the component statements and are false.

**(iii) **The component statements are:

100 is divisible by 3.

100 is divisible by 11.

100 is divisible by 5.

The component statements and are false whereas is true.