Mastering Set Theory for IIT JEE Main: Your Path to Success
Mastering Set Theory for IIT JEE Main Your Path to Success
Mastering Set Theory for IIT JEE Main: Your Path to Success
By Grandmaster Bikram Sutradhar, 5-Time World Record Holder Set Theory
www.sirbikramsutradhar.com
Unlocking Set Theory for JEE Excellence
Set Theory is not just a chapter—it’s a mathematical mindset. Foundational to Algebra, Probability, and Functions, this topic appears frequently in JEE Main. Whether it’s Venn diagrams, complement rules, or power sets, Set Theory challenges your logic, accuracy, and clarity.
I, Grandmaster Bikram Sutradhar, 5-Time World Record Holder, have distilled the essence of Set Theory into this guide—designed to help serious aspirants master even the toughest questions. Let’s make Set Theory your secret weapon. 🔓
Why Set Theory Matters in JEE Main
Set Theory forms the logical foundation for many math problems. Its concepts are applied in:
- Functions & Relations
- Probability
- Mathematical Reasoning
- Permutations & Combinations
It’s not only a scoring topic but also helps you build speed and precision.
Core Concepts You Must Master
🔹 What Is a Set?
A set is a collection of well-defined & distinct objects.
- Example: Vowels = {a, e, i, o, u}
🔹 Representation of Sets
- Roster Form: {2, 4, 6}
- Set-Builder Form: {x | x is even, x < 7}
🧠 Pro Tip: Use Set-Builder for infinite sets in proofs or theoretical problems.
Types of Sets
| Type | Example |
| Finite Set | {1, 2, 3, 4} |
| Infinite Set | {1, 2, 3, …} |
| Empty Set (∅) | {} |
| Singleton Set | {π} |
| Universal Set (U) | All elements in a context |
Subsets and Power Sets
- Subset (A ⊆ B): Every element of A is in B.
- Proper Subset (A ⊂ B): A is strictly smaller than B.
Example:
If A = {1, 2},
Then P(A) = {∅, {1}, {2}, {1, 2}} ⇒ 4 subsets (2²)
Equivalent Sets
- Equivalent Sets: Same cardinality, e.g., {1, 2} and {a, b}
⚠ JEE Trap: Don’t confuse equal with equivalent—many MCQs test this nuance!
Set Operations & Key Formulas
| Operation | Meaning | Example |
| Union (A ∪ B) | Elements in A or B or both | {1, 2} ∪ {2, 3} = {1, 2, 3} |
| Intersection (A ∩ B) | Elements common to both | {1, 2} ∩ {2, 3} = {2} |
| Complement (A′) | Elements in U but not in A | If U = {1–5}, A = {1, 2}, A′ = {3, 4, 5} |
| Difference (A – B) | Elements in A but not in B | {1, 2, 3} – {2} = {1, 3} |
| Symmetric Difference | A △ B = (B – A) ∪ (A – B) | {1, 2} △ {2, 3} = {1, 3} |
🔐 Cardinality Formulas
- For two sets:
n(A ∩ B) = n(A) + n(B) – n(A ∪ B) - For three sets:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(A∩C) + n(A∩B∩C)
Essential Laws to Remember
| Law | Formula |
| Commutative | A ∪ B = B ∪ A ; A ∩ B = B ∩ A |
| Associative | (A ∪ B) ∪ C = A ∪ (B ∪ C) |
| Distributive | A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) |
| De Morgan’s Laws | (A ∪ B)′ = A′ ∩ B′ ; (A ∩ B)′ = A′ ∪ B′ |
🔍 Challenging JEE-Level Examples
🔸 Example 1: Power Set Logic
Q: If A = {a, b}, how many proper subsets?
Sol: Total = 2² = 4 ⇒ Proper = 4 – 1 = 3
Answer: (b) 3
🔸 Example 2: Cardinality Word Problem
Q: In a class, 60% play cricket, 40% play football, 20% both. What % play neither?
Sol:
n(C ∪ F) = 60 + 40 – 20 = 80%
Neither = 100 – 80 = 20%
Answer: (a)
🔸 Example 3: De Morgan’s Verification
Q: U = {1–10}, A = {1, 3, 5, 7}, B = {2, 4, 6, 8}. Verify (A ∪ B)′ = A′ ∩ B′
Sol:
A ∪ B = {1–8} ⇒ (A ∪ B)′ = {9, 10}
A′ = {2, 4, 6, 8, 9, 10}, B′ = {1, 3, 5, 7, 9, 10}
A′ ∩ B′ = {9, 10}
Answer: (a)
🧠 High-Level Strategies for JEE Success
- Visualize with Venn Diagrams
Label intersections and complements clearly. - Memorize Core Identities
Especially De Morgan’s Laws & Cardinality Formulas. - Analyze Options Logically
Use elimination method for MCQs. - Avoid Concept Traps
Watch out for:- ∅ ≠ {0}
- Proper ⊂ vs Subset ⊆
- Equal vs Equivalent
- Practice Smart, Not Just Hard
Solve mixed-level MCQs, and time your problem-solving.
Final Words from Grandmaster Bikram Sutradhar
Set Theory is not just a topic—it’s a gateway to mathematical mastery. If you understand its principles, logic will never betray you in JEE Main.
Every formula here is a tool. Every solved example is a step toward your dream college.
For more insights, mock tests, and high-level problem-solving sessions, visit 👉 www.sirbikramsutradhar.com
Let’s rise. Let’s conquer.
— Grandmaster Bikram Sutradhar
Written By
Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar
bAstronautWay : A Government-Approved Trademark Brand
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Written By
Full Stack Developer and 5-Time World Record Holder, Grandmaster Bikram Sutradhar
bAstronautWay
SirBikramSutradhar on YouTube
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ICSE CLASS 10 ICSE CLASS 10 BIOLOGY BASTRONAUTWAY SirBikramSutradhar Bikram Sutradhar GrandMaster Bikram Sutradhar selina biology solutions ICSE Biology Selina Solution
📚 Class 9 Science – Complete Table of Contents (विषय-सूची)
CBSE | NCERT Curriculum | Bilingual (English + Hindi)
By Grandmaster Bikram Sutradhar | SirBikramSutradhar | BASTRONAUTWAY
🔬 PHYSICS (भौतिक विज्ञान)
| 🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
| 1️⃣ | Motion | गति | |
| 2️⃣ | Force and Laws of Motion | बल तथा गति के नियम | |
| 3️⃣ | Gravitation | गुरुत्वाकर्षण | |
| 4️⃣ | Work and Energy | कार्य तथा ऊर्जा | |
| 5️⃣ | Sound | ध्वनि |
🧪 CHEMISTRY (रसायन विज्ञान)
| 🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
| 1️⃣ | Matter in Our Surroundings | हमारे आस-पास के पदार्थ | |
| 2️⃣ | Is Matter Around Us Pure? | क्या हमारे आस-पास के पदार्थ शुद्ध हैं? | |
| 3️⃣ | Atoms and Molecules | परमाणु एवं अणु | |
| 4️⃣ | Structure of the Atom | परमाणु की संरचना |
🧬 BIOLOGY (जीव विज्ञान)
| 🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
| 1️⃣ | The Fundamental Unit of Life | जीवन की मौलिक इकाई | |
| 2️⃣ | Tissues | ऊतक | |
| 3️⃣ | Improvement in Food Resources | धनों में सुधार |
📘 ADDITIONAL SECTIONS (अतिरिक्त अनुभाग)
| 📖 Section | Title (English + Hindi) |
| 🔹 | Glossary / पारिभाषिक शब्दावली |
| 🔹 | Answer Keys / उत्तरमाला |
| 🔹 | Summary / सारांश |
| 🔹 | Important Diagrams / महत्वपूर्ण चित्र |
| 🔹 | NCERT Exercises / एनसीईआरटी अभ्यास |
| 🔹 | Sample Papers & MCQs / मॉडल पेपर व वस्तुनिष्ठ प्रश्न |
✅ All content follows the official NCERT Class 9 Science textbook structure. Each chapter will include explanations, bilingual notes, definitions, diagrams, MCQs, FAQs, and practice exercises under the BASTRONAUTWAY learning system.
class 10 Maths ncert solution.
CBSE Class 10 Mathematics (2025) NCERT Syllabus:
CBSE Class 10 Mathematics NCERT Syllabus (2025) – Chapter-Wise List
CBSE Class 10 Mathematics NCERT Syllabus (2025) – Chapter-Wise List
chapter 4. Quadratic Equations
chapter 5. Arithmetic Progressions
chapter 6. Triangles
chapter 7. Coordinate Geometry
chapter 8. Introduction to Trigonometry
chapter 9. Some Applications of Trigonometry
chapter 11. Areas Related to Circles
chapter 12. Surface Areas and Volumes
CBSE Class 10 Science (2025) NCERT Syllabus:
CBSE Class 10 Science NCERT Syllabus (2025) – Chapter-Wise List
CBSE Class 10 Science NCERT Syllabus (2025) – Chapter-Wise List
Chapter 1 Chemical Reactions and Equations
Chapter 2 Acids, Bases and Salts
Chapter 3 Metals and Non-metals
Chapter 4 Carbon and its Compounds
Chapter 5 Life Processes
Chapter 6 Control and Coordination
Chapter 7 How do Organisms Reproduce?
Chapter 8 Heredity
Chapter 9 Light – Reflection and Refraction
Chapter 10 The Human Eye and the Colourful World
Chapter 11 Electricity
Chapter 12 Magnetic Effects of Electric Current
Chapter 13 Our Environment
📖 Chapter 12 – Organic Chemistry (Selina Textbook)
Table of Contents:
- 12A. Organic Compounds
- 12B. Hydrocarbons: Alkanes
- 12C. Hydrocarbons: Alkenes
- 12D. Hydrocarbons: Alkynes
- 12E. Alcohols
- 12F. Carboxylic Acids
- Exercise 12 MISCELLANEOUS
- Glossary
- Model Question Paper –
📌 Exercise 12 MISCELLANEOUS – Focus Areas:
- 🧬 Consolidated practice from the entire Organic Chemistry chapter
- 🧪 Application-based questions covering alkanes, alkenes, alkynes, alcohols, and carboxylic acids
- 🧾 Writing structural formulas and chemical equations
- 💡 Distinguishing reactions, isomer identification, and conversions
- 📘 Full-syllabus revision to boost conceptual clarity and board exam readiness
Each question in this section is designed to:
- ✅ Strengthen cross-topic understanding
- 📝 Prepare students for application-based and reasoning-based questions
- 🧠 Improve problem-solving speed and exam performance
class 5
📚 Class 9 Science – Complete Table of Contents (विषय-सूची)
CBSE | NCERT Curriculum | Bilingual (English + Hindi)
By Grandmaster Bikram Sutradhar | SirBikramSutradhar | BASTRONAUTWAY
🔬 PHYSICS (भौतिक विज्ञान)
| 🔢 | Chapter Title (English) | अध्याय का नाम (हिंदी) | Page No. |
| 1️⃣ | Motion | गति | |
| 2️⃣ | Force and Laws of Motion | बल तथा गति के नियम |
