NCERT Solutions class-11 Maths Exercise 14.2

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.

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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.

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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.