NCERT Solutions class-11 Maths Exercise 14.2

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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.


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