RD Sharma Exercise 1.5 Solutions for Class 11 Maths covers the concept of the complement of a set, Venn diagrams, and related properties essential for CBSE students. This chapter lays a strong foundation in understanding how to deal with subsets, power sets, and universal sets through problem-solving. The exercise provides a variety of examples that help students develop critical thinking and a deeper grasp of set theory. Students aiming for strong marks in their Class 11 and competitive exams like JEE must master this topic.
In this post, you will find the step-by-step RD Sharma Class 11 Maths Exercise 1.5 Solutions, covering each question with logical explanations and diagrams where needed. A free YouTube video is also embedded to support visual learners. Moreover, we’ve added related Class 11 Maths study resources, important links, and downloadable PDF materials to enhance your preparation.
Key Highlights of RD Sharma Exercise 1.5 Class 11 Maths
- Topic: Complement of Sets and its Properties
- Based on: RD Sharma Class 11 Maths Chapter 1 – Sets
- Video Solutions: Watch on YouTube
- CBSE 2025-26 Curriculum Compatible
- Includes all solutions with explanation and Venn diagrams
- Useful for Class Tests, Annual Exams & Olympiads
- Linked to Class 11 Important Formulas and NCERT Solutions
📹 Video Solution – Exercise 1.5 Sets | RD Sharma Class 11
📚 Table of Contents
- Venn Diagram Concepts in Set Theory
- Complement of a Set with Examples
- Universal Set and Subsets
- Difference of Sets – Solved RD Sharma Questions
- Standard Set Identities – Proof-Based Questions
- Practice Tips for RD Sharma Sets Questions
Venn Diagram Concepts in Set Theory
Venn diagrams play a pivotal role in visualizing the relationships between different sets. In RD Sharma Exercise 1.5, many problems require students to understand the overlap, difference, and complement of sets using Venn representations. Venn diagrams help in simplifying complex set expressions by offering a clear picture of union, intersection, and complement regions.
Students often face confusion when dealing with three-set problems or questions involving universal sets. To overcome this, draw each region separately and label the parts clearly. For example, when given sets A, B, and the universal set U, sketch the shaded region representing A' ∩ B or A ∪ B'. This boosts conceptual clarity and aids in exam preparation.
Additionally, it is vital to recognize how Venn diagrams are used in logical reasoning problems for competitive exams like CUET, NDA, and JEE. Understanding how to translate a problem into a diagram reduces chances of mistakes and improves time management. If you're new to these diagrams, start by reviewing the NCERT Class 11 Solutions to build the base before diving into RD Sharma questions.
Complement of a Set with Examples
The complement of a set A, written as A', refers to all elements in the universal set U that are not in A. This fundamental concept appears in every problem in Exercise 1.5. A good grasp of complements is essential to handle more complex expressions like (A ∪ B)' or (A ∩ B)' using De Morgan’s laws.
For example, if U = {1,2,3,4,5} and A = {2,4}, then A' = {1,3,5}. Questions often involve solving set equations and interpreting results using Venn diagrams. Many students make errors while computing complements due to overlooking the universal set or overlapping elements.
It is advisable to memorize key properties such as A ∪ A' = U, A ∩ A' = Ø, and (A')' = A. These identities simplify problems quickly and are also useful in multiple-choice questions. Practice using Exercise 1.3 RD Sharma Solutions as a prerequisite to understand operations before jumping into complements.
Universal Set and Subsets
The universal set (U) contains all elements under consideration, and its definition is crucial when working with set complements and Venn diagrams. In RD Sharma Exercise 1.5, the universal set is often given or implied, and solving questions correctly depends on how well students can define and utilize U.
For instance, when asked to find A' ∩ B, students must first ensure that A and B are subsets of the same universal set. Failure to understand this leads to incorrect results. Problems in this section focus on identifying universal sets and differentiating them from other finite or infinite sets.
In Class 11, students also explore the idea of power sets and how subsets relate to each other. Practice more on this through the Class 11 Formula Sheet for a quick refresher. This will also help in solving short answer and assertion-reason type questions.
Difference of Sets – Solved RD Sharma Questions
The difference of two sets A and B, denoted by A - B, is the set of elements that belong to A but not to B. In RD Sharma Exercise 1.5, such problems are usually paired with complements and Venn diagrams for combined evaluation.
Students are expected to simplify expressions like (A - B)' or (B - A) ∪ C'. These questions test your understanding of set operations deeply and often come with two or more operations nested. Using set identities helps reduce such expressions systematically.
When working on such problems, it is important to refer to Venn diagrams and identify regions manually. If you struggle here, revisit Class 11 Important Questions based on RD Sharma for extra practice.
Standard Set Identities – Proof-Based Questions
Proof-based questions often test knowledge of standard set identities like distributive laws, De Morgan’s laws, and laws of complements. Exercise 1.5 includes many such questions where you're expected to prove that LHS = RHS using identities and logical steps.
Students must be careful while dealing with complements, unions, and intersections. Always start by writing down the identity and apply one rule at a time. For example, proving (A ∪ B)' = A' ∩ B' requires understanding of both the union operation and De Morgan’s law.
Review key formulas using the updated Class 11 Maths Syllabus to ensure you're covering all required proof types. These questions are likely to appear in both board and entrance exams.
Practice Tips for RD Sharma Sets Questions
To excel in RD Sharma Class 11 Exercise 1.5, consistent practice and revision of core set theory concepts are essential. Begin with the simplest one-mark questions and gradually take on proof-based and Venn diagram-based questions.
Use resources like Class 11 Maths Resources and watch the complete video walkthrough provided above. Mark all common identities on a separate sheet and revise them daily.
Lastly, after practicing from RD Sharma, cross-check your understanding with sample papers and NCERT exercises. You can also revise sets before moving into chapters like Limits and Derivatives here: Limits & Derivatives Class 11.
❓ Frequently Asked Questions (FAQs)
What is RD Sharma Exercise 1.5 about?
This exercise deals with complements of sets, Venn diagrams, and standard set identities for Class 11 students.
Is the YouTube solution free to watch?
Yes, the full video solution for Exercise 1.5 is available for free at this link.
Where can I find all Class 11 Maths formulas?
Visit this page for the complete formula sheet.
How important is this exercise for exams?
Very important. This exercise forms the base for advanced chapters and appears frequently in CBSE exams.
What type of questions are covered in Exercise 1.5?
It includes MCQs, descriptive, and proof-based problems based on complements and set identities.
Are Venn diagrams mandatory for solving?
Yes, in most cases Venn diagrams help solve the problems more effectively.
Where can I get CBSE Class 11 Syllabus 2025-26?
Visit this syllabus page for the latest updates.
How can I score full marks in Sets chapter?
Practice all RD Sharma problems and revise identities regularly. Use diagrams wherever possible.
Are the solutions matching the latest CBSE pattern?
Yes, these solutions are updated for the CBSE 2025-26 curriculum.
Where can I find more Class 11 Maths RD Sharma solutions?
Browse more exercises here.
📄 For official curriculum reference, visit the CBSE Academic Website.