NCERT Solutions for Class 11 Maths Chapter 1 Sets Ex 1.2

Exercise (1.2)

1. Which of the following are examples of the null set

i. Set of odd natural numbers divisible by $2$

Ans: Given that,

Set of odd natural numbers divisible by $2$

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

There is no odd number that will be divisible by $2$ and so this set is a null set.

$\therefore $The set of odd natural number divisible by $2$ is a null set.

ii. Set of even prime numbers

Ans: Given that,

Set of even prime numbers.

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

There was an even number $2$, will be the one and only even prime number. So the set contains an element. So it is not a null set.

$\therefore $The set of even prime numbers is not a null set.

iii. $\left\{ x:x\text{ is a natural numbers, x < 5 and x < 7} \right\}$

Ans: Given that,

$\left\{ x:x\text{ is a natural numbers, x < 5 and x < 7} \right\}$

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

There was no  number that will be less than $5$ and greater than $7$ simultaneously. So it is a null set

$\therefore $$\left\{ x:x\text{ is a natural numbers, x < 5 and x < 7} \right\}$ is a null set

iv. $\left\{ y:y\text{ is a point common to any two parallel lines} \right\}$

Ans: Given that,

$\left\{ y:y\text{ is a point common to any two parallel lines} \right\}$

To find if the given statement is an example of null set

A set which does not contain any element is called the empty set or the null set or the void set.

The parallel line does not intersect each other. So it does not have common point of intersection. So it is null set.

$\therefore $$\left\{ y:y\text{ is a point common to any two parallel lines} \right\}$is a null set.

2. Which of the following sets are finite or infinite.

i. The sets of months of a year

Ans: Given that,

The sets of months of a year

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

A year has twelve months which has defined number of elements

$\therefore $The set of months of a year is finite.

ii. $\left\{ 1,2,3... \right\}$

Ans: Given that,

$\left\{ 1,2,3... \right\}$

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

The set consists of infinite number of natural numbers.

$\therefore $The set $\left\{ 1,2,3... \right\}$ is infinite since it contains infinite number of elements.

iii. $\left\{ 1,2,3,...,99,100 \right\}$

Ans: Given that,

$\left\{ 1,2,3,...,99,100 \right\}$

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

This set contains the elements from $1$ to $100$which are finite in number.

$\therefore $The set $\left\{ 1,2,3,...,99,100 \right\}$ is finite.

iv. The set of positive integers greater than $100$

Ans: Given that,

The set of positive integers greater than $100$

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

The positive integers which are greater than $100$ are infinite in number.

$\therefore $The set of positive integers greater than $100$ is infinite.

v. The set of prime numbers less than $99$

Ans: Given that,

The set of prime numbers less than $99$

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

The prime numbers less than $99$ are finite in number.

$\therefore $The set of prime numbers less than $99$ is finite.

3. State whether each of the following set is finite or infinite:

i. The sets of lines which are parallel to $x$ axis

Ans: Given that,

The set of lines which are parallel to $x$ axis

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

The lines parallel to $x$ axis are infinite in number.

$\therefore $The set of line parallel to $x$ axis is infinite.

ii. The set of letters in English alphabet

Ans: Given that,

The set of letter sin English alphabet

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

English alphabet consist of $26$ elements which is finite in number

$\therefore $The set of letters in English alphabet is finite.

iii. The set of numbers which are multiple of $5$

Ans: Given that,

The set of numbers which are multiple of $5$

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

The numbers which are all multiple of $5$ are infinite in number.

$\therefore $The set of numbers which are multiple of $5$is infinite.

iv. The set of animals living on the earth

Ans: Given that,

The set of animals living on the earth

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

Although the number of animals on the earth is quite a big number, it is finite.

$\therefore $The set of animals living on the earth is finite.

v. The set of circles passing through the origin $\left( 0,0 \right)$

Ans: Given that,

The set of circles passing through the origin $\left( 0,0 \right)$

To find if the set is finite or infinite

A set which is empty or consists of definite number of elements is called finite otherwise the set is called infinite.

The number of circles passing through origin may be infinite in number.

$\therefore $The set of circles passing through origin $\left( 0,0 \right)$ is infinite.

4. In the following, state whether $A=B$ or not

i. $A=\left\{ a,b,c,d \right\};B=\left\{ d,c,b,a \right\}$

Ans: Given that,

$A=\left\{ a,b,c,d \right\};B=\left\{ d,c,b,a \right\}$

To state whether $A=B$

We know that the order in which the elements are listed are insignificant. So $A=B$

$\therefore A=B$

ii. $A=\left\{ 4,8,12,16 \right\}:B=\left\{ 8,4,16,18 \right\}$

Ans: Given that,

$A=\left\{ 4,8,12,16 \right\}:B=\left\{ 8,4,16,18 \right\}$

To state whether $A=B$

We know that $12\in A$ but $12\notin B$

$\therefore A\ne B$

iii. $A=\left\{ 2,4,6,8,10 \right\};B=\left\{ x:x\text{ is a positive integer and x}\le \text{10} \right\}$

Ans: Given that,

$A=\left\{ 2,4,6,8,10 \right\};B=\left\{ x:x\text{ is a positive integer and x}\le \text{10} \right\}$

To state whether $A=B$

$A=\left\{ 2,4,6,8,10 \right\}$

The positive integers less than $10$ are $B=\left\{ 1,2,3,4,5,6,7,8,9,10 \right\}$ So $A=B$

$\therefore A=B$

iv. $A=\left\{ x:x\text{ is a multiple of 10} \right\};B=\left\{ 10,15,20,25,30,... \right\}$

Ans: Given that,

$A=\left\{ x:x\text{ is a multiple of 10} \right\};B=\left\{ 10,15,20,25,30,... \right\}$

To state whether $A=B$

$A=\left\{ 10,20,30,40,... \right\}$

$B=\left\{ 10,15,20,25,30,... \right\}$

The elements of A consists only the multiples of $10$ and not of $5$. So $A\ne B$

$\therefore A\ne B$

5. Are the following pair of sets equal? Give reasons.

i. $A=\left\{ 2,3 \right\};B=\left\{ x:x\text{ is solution of }{{\text{x}}^{2}}+5x+6=0 \right\}$

Ans: Given that,

$A=\left\{ 2,3 \right\};B=\left\{ x:x\text{ is a solution of }{{\text{x}}^{2}}+5x+6=0 \right\}$

To state whether $A=B$

Solving ${{x}^{2}}+5x+6=0$,

${{x}^{2}}+3x+2x+6=0$

$\left( x+2 \right)\left( x+3 \right)=0$

$x=-2,-3$

$B=\left\{ -2,-3 \right\}$ and $A=\left\{ 2,3 \right\}$

So $A\ne B$

$\therefore A\ne B$

ii. $A=\left\{ x:x\text{ is a letter in the word FOLLOW} \right\};B=\left\{ y:y\text{ is a letter in the word WOLF} \right\}$

Ans: Given that,

$A=\left\{ x:x\text{ is a letter in the word FOLLOW} \right\};B=\left\{ y:y\text{ is a letter in the word WOLF} \right\}$

To state whether $A=B$

$A=\left\{ x:x\text{ is a letter in the word FOLLOW} \right\}=\left\{ F,O,L,W \right\}$

$B=\left\{ y:y\text{ is a letter in the word WOLF} \right\}=\left\{ W,O,L,F \right\}$

We know that the order in which the elements are listed are insignificant. So $A=B$

$\therefore A=B$

6. From the sets given below, select equal sets:

$A=\left\{ 2,4,8,12 \right\},B=\left\{ 1,2,3,4 \right\},C=\left\{ 4,8,12,14 \right\},D=\left\{ 3,1,4,2 \right\}$$E=\left\{ -1,1 \right\},F=\left\{ 0,a \right\},G=\left\{ 1,-1 \right\},H=\left\{ 0,1 \right\}$

Ans: Given that,

$A=\left\{ 2,4,8,12 \right\},B=\left\{ 1,2,3,4 \right\},C=\left\{ 4,8,12,14 \right\},D=\left\{ 3,1,4,2 \right\}$

$E=\left\{ -1,1 \right\},F=\left\{ 0,a \right\},G=\left\{ 1,-1 \right\},H=\left\{ 0,1 \right\}$

To select equal sets from the given set

Two sets A and B are said to be equal if they have exactly the same elements and we write A = B

We can observe from the sets that,

$8\in A,8\notin B,8\notin D,8\notin E,8\notin F,8\notin G,8\notin H$

And thus 

$A\ne B,A\ne D,A\ne E,A\ne F,A\ne G,A\ne H$

But $8\in C$

And checking other elements,

$2\in A,2\notin C$

So $A\ne C$

$3\in B,3\notin C,3\notin E,3\notin F,3\notin G,3\notin H$

And thus,

$B\ne C,B\ne E,B\ne F,B\ne G,B\ne H$

$12\in C,12\notin D,12\notin E,12\notin F,12\notin G,12\notin H$

And thus 

$C\ne D,C\ne E,C\ne F,C\ne G,C\ne H$

$4\in D,4\notin E,4\notin F,4\notin G,4\notin H$

And thus,

$D\ne E,D\ne F,D\ne G,D\ne H$

Similarly $E\ne F,E\ne G,E\ne H$

$F\ne G,F\ne H$

$G\ne H$

We know that the order of the elements I listed are insignificant.

So $B=D,E=G$

$\therefore $He equal sets are $B=D$ and $E=G$

NCERT Solution Class 11 Maths of Chapter 1 All Exercises

NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.2

NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.2 prepared by the expert Mathematics teacher at Vedantu is available here in the pdf format. Solutions to all the questions covered in the exercise are prepared by the experts as per the guidelines issued by the CBSE board. Download Class 11 Maths Chapter 1 Sets Ex 1.2 Questions with Solutions pdf to score good marks in your academic and competitive exams. The questions covered in this exercise are based on the topic “ The Empty Set, The Finite and Infinite Set, and Equal Set”.

Empty Set: The empty set, also known as a null or void set, is the set that does not contain any element.

Finite and Infinite Sets:  Finite sets are the sets that contain a finite number of elements in a set whereas the infinite sets are the sets that do not contain any definite number of elements.

Equal Sets: Two sets such as set X and set Y are said to be equal if they have exactly the same elements. This can be written as  X = Y.  On the other hand, if two sets X and Y do not contain the same number of elements, then it is termed unequal sets. Unequal sets are represented as X  ≠ Y

Opting for the NCERT solutions for Ex 1.2 Class 11 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 1.2 Class 11 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 11 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 11 Maths Chapter 1 Exercise 1.2 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 11 Maths Chapter 1 Exercise 1.2, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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