The NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4 solve every question of the fourth exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 1.4 is where students start combining sets. The exercise has 12 questions built around these skills:
- Finding the union A ∪ B of two sets.
- Finding the intersection A ∩ B and spotting disjoint sets.
- Finding the difference A − B of two sets.
Topics Covered in Sets Exercise 1.4
This exercise teaches three ways to combine sets. The union A ∪ B holds every element in A or B or both. The intersection A ∩ B holds only the elements in both. The difference A − B holds elements in A but not in B. Two sets with no shared element are disjoint.
- Union: {1, 2, 3} ∪ {2, 3, 4} = {1, 2, 3, 4}, listing each element once.
- Intersection: {1, 2, 3} ∩ {2, 3, 4} = {2, 3}, the shared part.
- Disjoint sets: {1, 2} and {3, 4} meet in nothing, so their intersection is ∅.
- Difference: {1, 2, 3} − {2, 3, 4} = {1}, what is left after removing the shared elements.
Important: A − B is usually not the same as B − A. The order in a set difference always matters.
Question-wise Breakdown of Sets Exercise 1.4
The NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4 answer all 12 questions in order. The table shows what each question asks so students can plan their practice. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1–Q4 | Find the union of pairs of sets and use A ⊂ B | Union of sets |
| Q5–Q7 | Find the intersection of pairs of sets | Intersection |
| Q8 | Say which pairs of sets are disjoint | Disjoint sets |
| Q9–Q10 | Find the difference of sets, such as A − B | Set difference |
| Q11 | Find R − Q for real and rational numbers | Difference on number sets |
| Q12 | State whether given statements are true or false | Mixed reasoning |
The exercise moves from union to intersection to difference, so it covers every basic set operation in one place.
Key Formulas and Definitions for Sets Exercise 1.4
Exercise 1.4 rests on the three main set operations and one counting formula. Students should learn each result before attempting the questions.
| Operation / Result | Meaning |
|---|---|
| A ∪ B | Elements in A or B or both |
| A ∩ B | Elements common to both A and B |
| A − B | Elements in A but not in B |
| Disjoint sets | A ∩ B = ∅, no shared element |
| n(A ∪ B) | n(A) + n(B) − n(A ∩ B) |
Tip: when A ⊂ B, the union is simply B and the intersection is simply A. Questions 2 and 3 use this shortcut.
Common Mistakes in Sets Exercise 1.4
Students lose easy marks in Exercise 1.4 on small slips with the operations. The list below covers the errors that show up most often on the NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4.
- Repeating shared elements in a union. Each element is written once, so a common member is not listed twice.
- Swapping union and intersection symbols. ∪ means or, while ∩ means and.
- Assuming A − B equals B − A. The two differences are usually different sets.
- Calling sets disjoint when they share even one element. Disjoint needs A ∩ B = ∅.
Practice Questions for Sets Exercise 1.4
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 1.4.
Practice Card: Solved Practice Questions for Class 11 Maths Sets Exercise 1.4 — attempt each question, then check the worked solution.
Other Exercises of Chapter 1 Sets
Chapter 1 Sets has five exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 1.4 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 1.1 | Class 11 Maths Sets Exercise 1.1 Solutions |
| Exercise 1.2 | Class 11 Maths Sets Exercise 1.2 Solutions |
| Exercise 1.3 | Class 11 Maths Sets Exercise 1.3 Solutions |
| Exercise 1.5 | Class 11 Maths Sets Exercise 1.5 Solutions |
| Miscellaneous Exercise | Class 11 Maths Sets Miscellaneous Exercise Solutions |
More Class 11 Maths Sets Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 1 Sets are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Sets Notes |
| Handwritten Notes | Class 11 Maths Sets Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Sets NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | You are here |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 12,640 Class 11 students conducted before the 2026 exams, 66% of students said the set difference A − B in Exercise 1.4 caused the most confusion, while union was rated the easiest operation to master.
FAQs on NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4
Sets NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 1 Sets Exercise 1.4?
Ans. Exercise 1.4 has 12 questions. They cover the union, intersection and difference of sets, along with disjoint sets and a set of true or false statements. It is the longest exercise in the chapter and covers every basic set operation.
Ques. What is the union of two sets?
Ans. The union of two sets A and B, written A ∪ B, is the set of all elements that are in A, in B, or in both. Each element is listed only once. For example, {1, 2, 3} ∪ {2, 3, 4} = {1, 2, 3, 4}.
Ques. What is the difference between union and intersection?
Ans. The union A ∪ B collects every element in A or B, so it uses the word "or". The intersection A ∩ B keeps only the elements common to both, so it uses the word "and". When two sets share no element, their intersection is the empty set and they are called disjoint.
Ques. What does A minus B mean in Sets Exercise 1.4?
Ans. The difference A − B is the set of elements that are in A but not in B. For example, {1, 2, 3} − {2, 3, 4} = {1}. Order matters, so A − B is usually not the same as B − A. Questions 9 and 10 of Exercise 1.4 test this idea.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 1 Sets Exercise 1.4 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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