RD Sharma Exercise 1.1 Solutions for Class 11 Maths – Detailed Answers and Explanations

Overview: Class 11 Maths begins with one of the most foundational topics — Sets. This chapter lays the groundwork for all major topics such as Relations and Functions, Probability, and more. RD Sharma’s Chapter 1 Exercise 1.1 is designed to help students gain a clear understanding of what a set is, how it is defined, and how to represent it. Below you’ll find detailed step-by-step solutions to each problem in this exercise along with explanations, tips, and embedded video support.

Table of Contents

• Introduction to Sets
• Key Concepts in Exercise 1.1
• RD Sharma Exercise 1.1 Solutions
• Watch Video Solutions
• How to Prepare for Sets
• Importance of Sets in Class 11 and Beyond
• Also Read
• FAQs

Introduction to Sets

In mathematics, a set is a collection of well-defined and distinct objects, considered as an object in itself. These objects are called elements or members of the set. Sets are typically denoted by capital letters and their elements by small letters.

Examples of sets:

• Set of natural numbers less than 10: {1, 2, 3, 4, 5, 6, 7, 8, 9}
• Set of vowels in the English alphabet: {a, e, i, o, u}
• Set of months in a year: {January, February, March, ...}

Key Concepts Covered in Exercise 1.1

This exercise focuses on identifying whether a collection is a set, representing sets in different forms, and understanding key types of sets. Here’s a quick breakdown:

• Well-defined collection: A set must be well-defined. This means it should be clear whether an object belongs to the set or not.
• Roster form: Listing out all elements separated by commas and enclosed within curly brackets.
• Set-builder form: Describing the properties that its members must satisfy.
• Types of sets: Finite, Infinite, Null, Singleton, Equal, Equivalent, etc.

RD Sharma Class 11 Maths Chapter 1 Exercise 1.1 Solutions

Q1. State which of the following are sets and justify your answer.

(i) The collection of all months of a year beginning with the letter J: Yes, it’s well-defined. It includes January, June, and July. Hence, it's a set.

(ii) The collection of ten most talented writers of India: Not a set. The term "most talented" is subjective.

(iii) A team of eleven best cricket batsmen of the world: Not a set. The word "best" is open to interpretation.

(iv) The collection of all girls in your class: It’s well-defined and countable. Hence, it's a set.

Q2. Write the following sets in roster form:

(i) A = {x : x is a natural number less than 6} = {1, 2, 3, 4, 5}

(ii) B = {x : x is a letter in the word ‘MATHS’} = {M, A, T, H, S}

(iii) C = {x : x is a vowel in the English alphabet} = {a, e, i, o, u}

(iv) D = {x : x is a whole number less than 5} = {0, 1, 2, 3, 4}

Q3. Write the following sets in set-builder form:

(i) {2, 4, 6, 8, 10} = {x : x is an even natural number less than or equal to 10}

(ii) {1, 4, 9, 16, 25} = {x : x = n², n ∈ N and n ≤ 5}

(iii) {a, e, i, o, u} = {x : x is a vowel in the English alphabet}

Watch Video Solutions

For a better understanding of these questions, watch the full video solution here:

How to Prepare for Sets in Class 11

• Step 1: Read the theory part of your NCERT and RD Sharma book thoroughly.
• Step 2: Understand definitions and key terms like finite/infinite, subset, power set, etc.
• Step 3: Solve all examples given in the book before starting the exercise questions.
• Step 4: Practice Venn diagrams to visually understand set relationships.
• Step 5: Use RD Sharma for mastering the application of set operations through a variety of questions.

Why Sets Are Important in Class 11 and Beyond

Sets are the base for many advanced mathematical topics such as:

• Relations and Functions: Definitions and domains are based on sets.
• Probability: Events are treated as sets.
• Venn Diagrams: Logical representations use sets extensively.
• Computer Science: Data structures and algorithms use set theory.

Also Read

• Class 11 Maths Syllabus 2025-26
• Comparing NCERT, RD Sharma, and RS Aggarwal
• Class 10 Maths All Formulas Chapter-wise

FAQs

What is the importance of studying sets in Class 11 Maths?

Understanding sets is fundamental as it forms the basis for topics like relations, functions, and probability.

How can I effectively prepare for questions on sets?

Practice RD Sharma, visualize with Venn diagrams, and refer to solution videos to reinforce concepts.

Is RD Sharma sufficient for Class 11 Maths preparation?

Yes, RD Sharma covers all essential concepts with examples and exercises of varying difficulty levels.

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