# NCERT Solutions for Exercise 1.3 Class 11 Maths Chapter 1 - Sets

In the previous exercises, you have already learned about the definitions of sets, representation of sets, different types of sets. In the NCERT solutions for Class 11 Maths chapter 1 exercise 1.3, you will learn about the three important concepts called subset, power set, and universal set. The power set of any set A i is defined as the collections of all subsets of set A. In the Class 11 Maths chapter 1 exercise 1.3 solutions, you will get the questions related to finding the subset and power set of the given set. First, go through the definitions ad examples given before the Class 11 Maths ch 1 ex 1.3. You will get a basic understanding of these concepts by solving the examples in the textbook. You can solve the Class 11th Maths chapter 1 exercise 1.3 problems by yourself. These questions are very basic based on the definitions of subsets and power sets. If you are looking for the NCERT solutions, click on the NCERT solutions given here. You will get NCERT solutions for Class 6 to Class 12.

**Also, see**

- Sets Exercise 1.1
- Sets Exercise 1.2
- Sets Exercise 1.4
- Sets Exercise 1.5
- Sets Exercise 1.6
- Sets Miscellaneous Exercise

**Sets Class 11 Chapter 1 Exercise:**** ****1.3**

Question:1 Make correct statements by filling in the symbols or in the blank spaces :

(i) { 2, 3, 4 } _____ { 1, 2, 3, 4,5 }

(ii) { a, b, c }______ { b, c, d }

(iii) {x : x is a student of Class XI of your school}______{x : x student of your school}

(iv) {x : x is a circle in the plane} ______{x : x is a circle in the same plane with radius 1 unit}

(v) {x : x is a triangle in a plane} ______ {x : x is a rectangle in the plane}

(vi) {x : x is an equilateral triangle in a plane} ______{x : x is a triangle in the same plane}

(vii) {x : x is an even natural number} _____ {x : x is an integer}

Answer:

A set A is said to be a subset of a set B if every element of A is also an element of B.

(i). All elements {2,3,4} are also elements of {1,2,3,4,5} .

So, {2,3,4} {1,2,3,4,5}.

(ii).All elements { a, b, c } are not elements of{ b, c, d }.

Hence,{ a, b, c } { b, c, d }.

(iii) Students of class XI are also students of your school.

Hence,{x : x is a student of Class XI of your school} {x : x student of your school}

(iv). Here, {x : x is a circle in the plane} {x : x is a circle in the same plane with radius 1 unit} : since a circle in the plane can have any radius

(v). Triangles and rectangles are two different shapes.

Hence,{x : x is a triangle in a plane} {x : x is a rectangle in the plane}

(vi). Equilateral triangles are part of all types of triangles.

So,{x : x is an equilateral triangle in a plane} {x : x is a triangle in the same plane}

(vii).Even natural numbers are part of all integers.

Hence, {x : x is an even natural number} {x : x is an integer}

Question:2 Examine whether the following statements are true or false:

(i) { a, b } { b, c, a }

(ii) { a, e } { x : x is a vowel in the English alphabet}

(iii) { 1, 2, 3 } { 1, 3, 5 }

(iv) { a } { a, b, c }

(v) { a } { a, b, c }

(vi) { x : x is an even natural number less than 6} { x : x is a natural number which divides 36}

Answer:

(i) All elements of { a, b } lie in { b, c, a }.So,{ a, b } { b, c, a }.

Hence,it is false.

(ii) All elements of { a, e } lie in {a,e,i,o,u}.

Hence,the statements given is true.

(iii) All elements of { 1, 2, 3 } are not present in { 1, 3, 5 }.

Hence,statement given is false.

(iv) Element of { a } lie in { a, b, c }.

Hence,the statement is true.

(v). { a } { a, b, c }

So,the statement is false.

(vi) All elements {2,4,} lies in {1,2,3,4,6,9,12,18,36}.

Hence,the statement is true.

Question:3(i) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

{3, 4} A

Answer:

3 {3,4} but 3 {1,2,{3,4},5}.

SO, {3, 4} A

Hence,the statement is incorrect.

Question:3(ii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

{3, 4} A

Answer:

{3, 4} is element of A.

So, {3, 4} A.

Hence,the statement is correct.

Question:3(iii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

{{3, 4}} A

Answer:

Here,

{ 3, 4 } { 1, 2, { 3, 4 }, 5 }

and { 3, 4 } {{3, 4}}

So, {{3, 4}} A.

Hence,the statement is correct.

Question:3(iv) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

1 A

Answer:

Given, 1 is element of { 1, 2, { 3, 4 }, 5 }.

So,1 A.

Hence,statement is correct.

Question:3(v) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

1 A

Answer:

Here, 1 is element of set A = { 1, 2, { 3, 4 }, 5 }.So,elements of set A cannot be subset of set A.

1 { 1, 2, { 3, 4 }, 5 }.

Hence,the statement given is incorrect.

Question:3(vi) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

{1,2,5} A

Answer:

All elements of {1,2,5} are present in { 1, 2, { 3, 4 }, 5 }.

So, {1,2,5} { 1, 2, { 3, 4 }, 5 }.

Hence,the statement given is correct.

Question:3(vii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

{1,2,5} A

Answer:

Here,{1,2,5} is not an element of { 1, 2, { 3, 4 }, 5 }.

So,{1,2,5} A .

Hence, statement is incorrect.

Question:3(viii) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

{1,2,3} A

Answer:

Here, 3 {1,2,3}

but 3 { 1, 2, { 3, 4 }, 5 }.

So, {1,2,3} A

Hence,the given statement is incorrect.

Question:3(ix) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

Answer:

is not an element of { 1, 2, { 3, 4 }, 5 }.

So,.

Hence,the above statement is incorrect.

Question:3(x) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

Answer:

is subset of all sets.

Hence,the above statement is correct.

Question:3(xi) Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?

Answer:

{ 1, 2, { 3, 4 }, 5 }. but is not an element of { 1, 2, { 3, 4 }, 5 }.

Hence, the above statement is incorrect.

Question:4(ii) Write down all the subsets of the following sets:

{a, b}

Answer:

Subsets of . Thus the given set has 4 subsets

Question:4(iv) Write down all the subsets of the following sets:

Answer:

Subset of is only.

The subset of a null set is null set itself

Question:5 How many elements has P(A), if A = ?

Answer:

Let the elements in set A be m, then n m

then, the number of elements in power set of A n

Here, A = so n 0

n 1

Hence,we conclude P(A) has 1 element.

Question:6 Write the following as intervals :

(i) {x : x R, – 4 x 6}

(ii) {x : x R, – 12 x –10}

(iii) {x : x R, 0 x 7}

(iv) {x : x R, 3 x 4}

Answer:

The following can be written in interval as :

(i) {x : x R, – 4 x 6}

(ii) {x : x R, – 12 x –10}

(iii) {x : x R, 0 x 7}

(iv) (iv) {x : x R, 3 x 4}

Question:7 Write the following intervals in set-builder form :

(i) (– 3, 0)

(ii) [6 , 12]

(iii) (6, 12]

(iv) [–23, 5)

Answer:

The given intervals can be written in set builder form as :

(i) (– 3, 0)

(ii) [6 , 12]

(iii) (6, 12]

(iv) [–23, 5)

Question:8 What universal set(s) would you propose for each of the following :

(i) The set of right triangles.

(ii) The set of isosceles triangles.

Answer:

(i) Universal set for a set of right angle triangles can be set of polygons or set of all triangles.

(ii) Universal set for a set of isosceles angle triangles can be set of polygons.

**More About NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3:-**

In Class 11th Maths chapter 1 exercise 1.3, there are nine questions related to finding the subsets and power sets of the given set. Before the Class 11th Maths chapter 1 exercise 1.3, there are some examples and definitions given in the NCERT textbook. You can solve these examples and then questions from this exercise.

**Also Read| **Sets Class 11th Notes

**Benefits of NCERT Solutions for Class 11 Maths Chapter 1 Exercise 1.3:-**

- NCERT syllabus Class 11th Maths chapter 1 exercise 1.3 is based on the basics of the set, subsets, and power set. These concepts are not difficult but required understanding the many concepts in maths.
- As the knowledge of sets is required to understand the concept of probability, the Class 11 Maths chapter 1 exercise 1.3 solutions are very helpful.
- NCERT solutions for Class 11 Maths chapter 1 exercise 1.3 can be used for the revision of the important concepts of sets.

**Also see-**

**NCERT Solutions of Class 11 Subject Wise**

**Subject Wise NCERT Exampler Solutions**

Happy learning!!!

## Frequently Asked Question (FAQs) - NCERT Solutions for Exercise 1.3 Class 11 Maths Chapter 1 - Sets

**Question: **What is the subset ?

**Answer: **

Set B is said to be a subset of set A if every element of set B is present in set A.

**Question: **If the set A has 2 elements than find the number of elements in the power set of A ?

**Answer: **

Number of elements in the power set of A = 2^n = 2^2 = 4

**Question: **Find the power set of set A = {1} ?

**Answer: **

P(A) = { φ,{ 1 }}

**Question: **Find the subsets of set A = {1,2}

**Answer: **

Subsets of set A = φ,{ 1 }, { 2 }, { 1,2 }

**Question: **Find the subsets of set A = {1}

**Answer: **

Subsets of set A = φ,{ 1 }

**Question: **If the A is empty set than find the number of elements in the power set of A ?

**Answer: **

Number of elements in the power set of A = 2^n = 2^0 = 1

**Question: **Find the subsets of set A = φ

**Answer: **

Subsets of set A = φ

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