NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4 - PDF Download

NCERT solutions class 11 maths chapter 1 ex 1.4 stes covers essencial concepts of venn diagrams, union of sets, intersection of sets and difference of sets. In these solutions, the questions are designed to help students understand the properties associated with the union and the intersection of sets better. In addition, students learn about the venn diagram, which is a pictorial representation of these two concepts. 

Ex 1.4 class 11 maths chapter 1 solutions consist of a total of 12 questions and these questions are based on the use of operations mentioned above. Class 11 maths chapter 1 exercise 1.4 NCERT solutions developed by expert teachers of eSaral who have years of experience in the field of mathematics. NCERT solutions for ex 1.4 class 11 maths ch 1 help students to grab a thorough understanding of the topics associated with the exercise 1.4. NCERT solutions for class 11 maths chapter 1 ex 1.4 are available in PDF format. You can download the free PDF of these solutions from the eSaral website to prepare for your final exams. Download the PDF from the link provided below. 

Topics Covered in Exercise 1.4 Class 11 Mathematics Questions

In ex 1.4 class 11 maths ch 1 sets, we will discuss some important topics such as venn diagrams, union of sets, intersection of sets and difference of sets. 

1. Venn Diagrams - A diagram that shows all the possible relations between different sets. Any closed figure, like a circle or a polygon, can be used to represent a Venn diagram. Most of the time, we just use circles to represent the different sets.

The universal set is represented usually by a rectangle and its subsets by circles.

You will see an extensive use of the venn diagrams when we discuss the union, intersection and difference of sets.

2. Operations on Sets

The set operations are performed on at least two sets to get the combination of elements according to the operation performed on them.

There are three main types of operations that can be performed on a set in a set theory, namely:

• Union of Sets

• Intersection of Sets

• Difference of Sets
  

• Union of Sets - The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). In symbols, we write. A ∪ B = { x : x ∈A or x ∈B } 

The symbol ‘∪’ is used to denote the union. Symbolically, we write A ∪ B and usually read as ‘A union B’. The union of two sets can be represented by a Venn diagram.

For example - Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}, then we will have A ∪ B = { 2, 4, 6, 8, 10, 12}

Some Properties of the Operation of Union 

(I) A ∪ B = B ∪ A (Commutative law)

(II) ( A ∪ B ) ∪ C = A ∪ ( B ∪ C) (Associative law )

(III) A ∪ φ = A (Law of identity element, φ is the identity of ∪)

(IV) A ∪ A = A (Idempotent law)

(V) U ∪ A = U (Law of U)

• Intersection of Sets - The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, this operation is represented by 

A ∩ B = {x : x ∈ A and x ∈ B}

Where x is the common element of set A and B. 

If A and B are two sets such that A ∩ B = ϕ, then A and B are called disjoint sets. The disjoint sets can be represented by means of the Venn diagram.

Some Properties of Operation of Intersection

(I) A ∩ B = B ∩ A (Commutative law).

(II) ( A ∩ B ) ∩ C = A ∩ ( B ∩ C ) (Associative law).

(III)) ϕ∩ A = ϕ, U ∩ A = A (Law of ϕ and U). 

(IV) A ∩ A = A (Idempotent law)

(V) A ∩ ( B ∪ C ) = ( A ∩ B ) ∪ ( A ∩ C ) (Distributive law ).

• Difference of Sets - The difference of the sets A and B in this order is the set of elements which belong to A but not to B. Symbolically, we write A – B and read as “A minus B”.

We can write the definition in symbolically : A – B = { x : x ∈ A and x ∉ B }. The difference of two sets A and B can be represented by a Venn diagram.

Tips for Solving Exercise 1.4 Class 11 Chapter 1 Sets

Students can quickly learn the venn diagrams and operations of sets by going through the tips provided in NCERT solutions class 11 maths chapter 1 exercise 1.4. 

1. NCERT solutions for class 11 maths chapter 1 ex 1.4 will provide you with the foundational knowledge you need to master all the concepts to solve the questions.

2. Students should comprehend and learn the detailed explanation of operations of sets provided in the NCERT solutions class 11 maths chapter 1 ex 1.4. This will allow them to go through the entire exercise in a short time.

3. With NCERT solutions, questions practice and revision, you can easily prepare for exams.
   

Importance of Solving Ex 1.4 Class 11 Maths Chapter 1 Sets

You will get tremendous benefits by solving ex 1.4 class 11 maths chapter 1 sets. You can find all of them below.

1. Ex 1.4 class 11 math chapter 1 of NCERT solutions is essential in order to gain a basic understanding of Venn's diagram, which is a fundamental concept for the solution of questions concerning relations between sets and probability.  

2. Ex 1.4 in class 11 maths chapter 1 provides different ways of solving the problems.

3. Subject matter experts of eSaral have solved all the questions with easy tips and tricks which will help you to solve ex 1.4 with ease.

4. Practicing questions with NCERT solutions will save your time in exams and also boost your self-confidence.
   

Frequently Asked Questions

Question 1. What are union sets?

Answer 1. The union of two sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). In symbols, we write  A ∪ B = { x : x ∈A or x ∈B }. Symbolically, we write A ∪ B and usually read as ‘A union B’. 

Question 2. Write an example for union of sets?

Answer 2. If A = { a, e, i, o, u } and B = { a, i, u }, then A ∪ B = { a, e, i, o, u } = A. 

Question 3. What is the intersection of sets?

Answer 3. The intersection of two sets A and B is the set of all those elements which belong to both A and B. Symbolically, this operation is represented by 

A ∩ B = {x : x ∈ A and x ∈ B}.