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

NCERT solutions class 11 maths chapter 1 ex 1.3 Sets focuses on the concepts of subsets and universal sets. This includes questions related to the proper representation of statements by the use of appropriate symbols. Symbols in set theory are used to express statements about subsets and related terms. Here are a few examples in NCERT solutions class 11 maths chapter 1 ex 1.3 to help you understand how to use symbols in a set. 

Class 11 maths chapter 1 exercise 1.3 NCERT solutions have 8 questions with sub-parts. All 8 questions can be found in different formats like true-false, short answer, and long answer type questions. Ex 1.3 class 11 math chapter 1 solutions has plenty of problems to help you get through the topics quickly. Ex 1.3 class 11 maths chapter 1 NCERT solutions are designed by subject experts of eSaral which provides complete knowledge of topics and concepts of subsets and universal sets. NCERT solution PDFs are also available on eSaral. You can download the free PDF of these solutions to prepare for examinations. The link is provided below to download the PDF. 

Topics Covered in Exercise 1.3 Class 11 Mathematics Questions

Ex 1.3 class 11 maths chapter 1 NCERT solutions are based on the subsets, subsets of sets of real numbers, intervals as subsets of R, universal set. Find the thorough comprehension of these topics provided by the academic team of mathematics at eSaral.

1.  Subsets - A set A is said to be a subset of a set B if every element of A is also an element of B. Basically, A ⊂ B if whenever a ∈ A, then a ∈ B. It is often convenient to use the symbol “⇒” which means implies. Using this symbol, we can write the definition of subset as follows:

 A ⊂ B if a ∈ A ⇒ a ∈ B

We read the above statement as “A is a subset of B if a is an element of A implies that a is also an element of B”. 

• Subsets of set of real numbers 

Here are many important subsets of R and they are:

The set of natural numbers N = {1, 2, 3, 4, 5, . . .}.

The set of integers Z = {. . ., –3, –2, –1, 0, 1, 2, 3, . . .}.

The set of rational numbers Q = { x : x = p/q , p, q ∈ Z and q ≠ 0}.

The set of irrational numbers, denoted by T, is composed of all other real numbers. Thus T = {x : x ∈ R and x ∉ Q}, i.e., all real numbers that are not rational. Members of T include √2 , √5 and π. 

Some of the obvious relations among these subsets are:

N ⊂ Z ⊂ Q, Q ⊂ R, T ⊂ R, N ⊄ T.

• Intervals as subsets of R

Let a, b ∈ R and a < b. Then the set of real numbers { y : a < y < b} is called an open interval and is denoted by (a, b). All the points between a and b belong to the open interval (a, b) but a, b themselves do not belong to this interval. 

The interval which contains the end points also is called closed interval and is denoted by [ a, b ]. So [ a, b ] = {x : a ≤ x ≤ b}

Here, you can find intervals closed at one end and open at the other,

[ a, b ) = {x : a ≤ x < b} is an open interval from a to b, including a but excluding b.

( a, b ] = { x : a < x ≤ b } is an open interval from a to b including b but excluding a.

These intervals can be represented on the real number line.

2. Universal Set - A universal set is a collection that contains elements of all related sets without any repeating elements. The universal set is usually denoted by U. for example, if A and B are two sets, such as A = {1,2,3} and B = {1,a,b,c}, then the universal set associated with these two sets is given by U = {1,2,3,a,b,c}. 

There is no formula for finding the universal set. All we need to do is represent all the elements together as a single set, which we refer to as a universal set.

Tips for Solving Exercise 1.3 Class 11 Chapter 1 Sets 

Ex 1.3 class 11 maths ch 1 in NCERT solutions is a comprehensive guide that provides a deep understanding of each concept that is related to the sets, subsets, and symbols in sets. To solve questions of ex 1.3 and understand essential concepts, our expert faculty of eSaral has provided some really important tips.

1. These solutions have an easy-to-understand format. By solving questions step-by-step with examples in these solutions will help students easily understand complex topics.

2. Before solving the questions in this exercise, students should be able to solve any doubts they may have about the fundamental concepts of sets.

3. Students should learn and comprehend the significant topics associated with ex 1.3 before jumping into the questions of ex 1.3 class 11 maths. 
   

Importance of Solving Ex 1.3 Class 11 Maths Chapter 1 Sets

Solving questions of ex 1.3 class 11 maths chapter 1 sets will help you in preparing for exams. We have put together some of the important advantages of solving ex 1.3. Students can check them here.

1. By solving ex 1.3 class 11 maths NCERT solutions provided by eSaral, students will get an idea of all types of questions related to concepts associated with exercise 1.3.

2. NCERT solutions for class 11 maths chapter 1 assist students in developing a solid conceptual basis, which is essential for solving ex 1.3 questions for exam preparation.

3. These solutions provide in-depth understanding of subsets and universal sets which helps you to solve complex questions included in ex 1.3 class 11 maths.

4. NCERT solutions PDF will help you to check your answers to the questions which boost your confidence.
   

Frequently Asked Questions

Question 1. What is the universal set?

Answer 1. A universal set is a collection that contains elements of all related sets without any repeating elements. The universal set is usually denoted by U.

Question 2. Write an example of subsets?

Answer 2. The set Q of rational numbers is a subset of the set R of real numbers, and we write Q ⊂ R.