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

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

Edited By Vishal kumar | Updated on Nov 01, 2023 08:46 AM IST

## NCERT Solutions for Class 11 Maths Chapter 1: Sets Exercise 1.3- Download Free PDF

In the previous exercises, you have already learned about the definitions of sets, the representation of sets, and 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 and 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 NCERT solutions, click on the NCERT solutions given here. You will get NCERT solutions for Class 6 to Class 12.

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## Access sets Class 11 Chapter 1 Exercise: 1.3

(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}

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} $\subset$ {1,2,3,4,5}.

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

Hence,{ a, b, c } $\not\subset${ 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} $\subset$ {x : x student of your school}

(iv). Here, {x : x is a circle in the plane} $\not\subset$ {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} $\not\subset$ {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} $\subset$ {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} $\subset$ {x : x is an integer}

(i) { a, b } $\not\subset$ { b, c, a }

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

(iii) { 1, 2, 3 } $\subset$ { 1, 3, 5 }

(iv) { a } $\subset$ { a, b, c }

(v) { a } $\in$ { a, b, c }

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

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

{3, 4} $\subset$ A

3 $\in$ {3,4} but 3$\notin$ {1,2,{3,4},5}.

SO, {3, 4} $\not \subset$ A

Hence,the statement is incorrect.

{3, 4} $\in$ A

{3, 4} is element of A.

So, {3, 4} $\in$ A.

Hence,the statement is correct.

{{3, 4}} $\subset$ A

Here,

{ 3, 4 }$\in$ { 1, 2, { 3, 4 }, 5 }

and { 3, 4 } $\in$ {{3, 4}}

So, {{3, 4}} $\subset$ A.

Hence,the statement is correct.

1 $\in$ A

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

So,1 $\in$ A.

Hence,statement is correct.

1 $\subset$ A

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

1 $\not\subset$ { 1, 2, { 3, 4 }, 5 }.

Hence,the statement given is incorrect.

{1,2,5}$\subset$ A

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

So, {1,2,5}$\subset$ { 1, 2, { 3, 4 }, 5 }.

Hence,the statement given is correct.

{1,2,5} $\in$ A

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

So,{1,2,5} $\notin$A .

Hence, statement is incorrect.

{1,2,3} $\subset$ A

Here, 3$\in$ {1,2,3}

but 3 $\notin$ { 1, 2, { 3, 4 }, 5 }.

So, {1,2,3} $\not \subset$ A

Hence,the given statement is incorrect.

$\phi \in A$

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

So,$\phi \notin A$.

Hence,the above statement is incorrect.

$\phi \subset A$

$\phi$ is subset of all sets.

Hence,the above statement is correct.

$\left \{ \phi \right \} \subset A$

$\phi$ $\subset$ { 1, 2, { 3, 4 }, 5 }. but $\phi$ is not an element of { 1, 2, { 3, 4 }, 5 }.

$\left \{ \phi \right \} \not\subset A$

Hence, the above statement is incorrect.

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

{a}

Subsets of $\left \{ a \right \} = \phi \, and \left \{ a \right \}$.

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

{a, b}

Subsets of $\left \{ a,b \right \}\ are \ \phi , \left \{ a \right \},\left \{ b \right \} and \left \{ a,b \right \}$. Thus the given set has 4 subsets

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

{1,2,3}

Subsets of

$\left \{ 1,2,3 \right \} = \left \{ 1 \right \},\left \{ 2 \right \},\left \{ 3 \right \},\phi ,\left \{ 1,2 \right \},\left \{ 2,3 \right \},\left \{ 3,1 \right \},\left \{ 1,2,3 \right \}$

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

$\phi$

Subset of $\phi$ is $\phi$ only.

The subset of a null set is null set itself

Let the elements in set A be m, then n$\left ( A \right ) =$ m

then, the number of elements in power set of A n$\left ( p\left ( A \right )\right ) =$ $2^{m}$

Here, A = $\phi$ so n$\left ( A \right ) =$ 0

n$\left [ P\left ( A \right ) \right ] =$ $2^{0}$ $=$1

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

Question:6 Write the following as intervals :

(i) {x : x $\in$R, – 4 $<$ x $\leq$ 6}

(ii) {x : x $\in$ R, – 12 $<$x $<$–10}

(iii) {x : x $\in$ R, 0 $\leq$ x $<$ 7}

(iv) {x : x $\in$ R, 3 $\leq$ x $\leq$ 4}

The following can be written in interval as :

(i) {x : x $\in$R, – 4 $<$ x $\leq$ 6} $= \left ( -4 ,6 \right ]$

(ii) {x : x $\in$ R, – 12 $<$x $<$–10} $= \left ( -12,-10 \right )$

(iii) {x : x $\in$ R, 0 $\leq$ x $<$ 7} $= [ 0,7)$

(iv) (iv) {x : x $\in$ R, 3 $\leq$ x $\leq$ 4} $=\left [ 3,4 \right ]$

(i) (– 3, 0)

(ii) [6 , 12]

(iii) (6, 12]

(iv) [–23, 5)

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

(i) (– 3, 0) $= \left \{ x:x\in R, -3< x< 0 \right \}$

(ii) [6 , 12] $= \left \{ x:x\in R, 6\leq x\leq 12\right \}$

(iii) (6, 12] $= \left \{ x:x\in R, 6< x\leq 12\right \}$

(iv) [–23, 5)$= \left \{ x:x\in R, -23 \leq x< 5\right \}$

(i) The set of right triangles.

(ii) The set of isosceles triangles.

(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 11th class maths exercise 1.3 answers 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.

## Key Features of 11th Class Maths Exercise 1.3 Answers

1. Expertly Prepared: The ex 1.3 class 11 solutions are meticulously crafted by subject experts with a deep understanding of mathematics concepts.

2. CBSE Syllabus Alignment: The solutions adhere to the latest CBSE syllabus, ensuring that they cover all the relevant topics and concepts.

3. Comprehensive Coverage: Class 11 maths ex 1.3 includes a wide range of problems and questions, providing students with practice on various aspects of sets.

4. Structured Approach: The class 11 ex 1.3 solution follows a logical and step-by-step problem-solving method, making it easier for students to understand and apply the concepts.

5. Clarity and Explanation: Each 11th class maths exercise 1.3 answers is explained in a clear and concise manner, helping students understand the underlying concepts.
6. Preparation for Exams: These solutions are a valuable resource for students preparing for their exams, as they provide ample practice to enhance their problem-solving skills.
7. Online Availability: NCERT Solutions for Class 11 Maths are often available online in various formats, including PDFs, making them accessible to a wide range of students.
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## Subject Wise NCERT Exampler Solutions

Happy learning!!!

1. What is the subset ?

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

2. If the set A has 2 elements than find the number of elements in the power set of A ?

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

3. Find the power set of set A = {1} ?

P(A) = { φ,{ 1 }}

4. Find the subsets of set A = {1,2}

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

5. Find the subsets of set A = {1}

Subsets of set A = φ,{ 1 }

6. If the A is empty set than find the number of elements in the power set of A ?

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

7. Find the subsets of set A = φ

Subsets of set A = φ

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