# NCERT Solutions For Class 11 Maths Chapter 14 Exercise 14.2

## Chapter 14 Ex.14.2 Question 1

Write the negation of the following statements:

(i) Chennai is the capital of Tamil Nadu.

(ii) $$\sqrt 2$$ 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.

### Solution

(i) Chennai is not the capital of Tamil Nadu.

(ii) $$\sqrt 2$$ is a complex number.

(iii) All triangles are equilateral triangles.

(iv) The number $$2$$ is not greater than $$7$$.

(v) Every natural number is not an integer.

## Chapter 14 Ex.14.2 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.

(ii) The number $$x$$ is a rational number.

The number $$x$$ is an irrational number.

### Solution

(i) The negation of the first statement is ‘the number $$x$$ is a rational number’. This is same as the second statement. This is because if a number is not an irrational number, then it is a rational number.

Therefore, the given pairs of statements are negations of each other.

(ii) The negation of the first statement is ‘the number $$x$$ is not a rational number’. This means that the number $$x$$ is an irrational number, which is the same as the second statement. Therefore, the given pairs of statements are negations of each other.

## Chapter 14 Ex.14.2 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.

(ii) All integers are positive or negative.

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

### Solution

(i) The component statements are as follows.

$$\rm{p:}$$ Number $$3$$ is prime.

$$\rm{q:}$$ Number $$3$$ is odd.

Both the statements are true.

(ii) The component statements are as follows.

$$\rm{p:}$$ All integers are positive.

$$\rm{q:}$$ All integers are negative.

Both the statements are false.

(iii) The component statements are as follows.

$$\rm{p:}$$ $$100$$ is divisible by $$3.$$

$$\rm{q:}$$ $$100$$ is divisible by $$11.$$

$$\rm{r:}$$ $$100$$ is divisible by $$5.$$

Here the statements $$\rm{p}$$ and $$\rm{q}$$ are false and statement $$\rm{r}$$ is true.

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