Sets Class 6 ICSE — Maths Chapter 28 (Operations on Sets)
Operations on sets Class 6 ICSE teaches you how to combine two or more sets into a single set that satisfies a given condition. The chapter covers three operations: union of sets, intersection of sets, and difference of two sets. Each section below explains one operation in the book’s own order, with definitions, symbols, and worked examples, so you can read along with the chapter open.
Download Operations on Sets Class 6 ICSE Mathematics Chapter 28 PDF
Download the Operations on Sets Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 6 pages, 4 sections, 18 questions.
What is inside Chapter 28
6 pages · 4 sections · 12 worked examples · 18 exercise questions
| Section | Title |
|---|---|
| 28.1 | INTRODUCTION |
| 28.2 | UNION OF SETS |
| 28.3 | INTERSECTION OF SETS |
| 28.4 | DIFFERENCE OF TWO SETS |
- EXERCISE 28(A): 5 questions
- EXERCISE 28(B): 13 questions
28.1 INTRODUCTION
An operation on sets takes two or more sets and combines them into one set under a fixed rule. The result is always a single new set. This is the core idea of the whole chapter.
The chapter discusses three combining operations: union of sets, intersection of sets, and difference of two sets. Each operation has its own definition and its own symbol. You will meet each one in turn in the sections that follow.
Why learn these operations? Because they give you a clean way to build new sets from old ones. Instead of listing every element by hand, you apply one rule and read off the answer. The rest of the chapter builds on this idea, so the definition matters more than the examples.
Before you operate on any sets, you need to write them correctly. If you are unsure how sets are named and written, review the chapter on types of sets first.
28.2 UNION OF SETS
The union of two sets is the smallest set that contains every element of both given sets, with no element repeated. “Smallest” means the new set holds exactly the elements of the two sets and nothing extra.
The symbol for union is ∪. The union of sets A and B is written A \cup B. The same rule applies to any pair of sets, so the union of P and Q is P \cup Q, and so on.
The word “smallest” matters. If any element of either set is missing, the result fails to contain both sets. If a foreign element is added, the result is bigger than it should be. The union keeps every element of both sets, once each.
Take X = {2, 4, 6, 8} and Y = {4, 8, 10}. Both sets share 4 and 8, but the union writes them only once. X \cup Y = \{2, 4, 6, 8, 10\}. Every element of X and every element of Y is present, with no repetition.
28.3 INTERSECTION OF SETS
The intersection of two sets is the largest set of elements common to both sets. “Common” means the element appears in both sets at the same time. The symbol is ∩, so the intersection of A and B is written A \cap B.
Worked example: A = {1, 2, 3, 4} and B = {3, 4, 5}. The elements 3 and 4 appear in both sets. So A \cap B = \{3, 4\}.
If the given sets are in description form or set-builder form, convert them into roster form before operating. For example, “multiples of 3 between 1 and 20” becomes {3, 6, 9, 12, 15, 18}. Only then can you pick out the common elements.
Union and intersection with the empty set follow fixed rules. A \cup \phi = A, so union with the empty set gives the set itself. A \cap \phi = \phi, so intersection with the empty set gives the empty set. That is because the empty set adds no elements and shares no elements.
Two sets with no element in common are disjoint sets, and their intersection is empty. Two sets that share at least one element are overlapping sets, and their intersection is not empty. A common mistake is swapping the two symbols: ∪ collects everything, ∩ keeps only the shared part.
28.4 DIFFERENCE OF TWO SETS
The difference of two sets A and B is written in two ways: A - B or B - A. The set A - B holds the elements of A that do not belong to B. The set B - A holds the elements of B that do not belong to A.
Order decides the answer. A - B keeps only elements from A, while B - A keeps only elements from B. The two results are usually different sets, so you cannot swap them.
Worked example with words: A = letters of “RATNA” = {r, a, t, n} and B = letters of “TAN” = {t, a, n}. Every letter of B appears in A. So A - B = \{r\}, the only letter in A but not in B, and B - A = \phi, because nothing in B is missing from A.
The table below compares the three operations at a glance. Union gathers everything once. Intersection keeps only what is shared. Difference keeps the leftovers of the first set only.
| Operation | Symbol | Result contains |
|---|---|---|
| Union | \cup | Every element of both sets, no repeats |
| Intersection | \cap | Only the elements common to both sets |
| Difference A - B | - | Elements of A that are not in B |
What to practise from Operations on Sets Class 6 ICSE
This Class 6 ICSE chapter gives you two exercise blocks. Work through both in order, because the second one mixes all three operations together.
- EXERCISE 28(A) — 5 questions. These cover union, intersection, true or false statements on disjoint and overlapping sets, and combined operations.
- EXERCISE 28(B) — 13 questions. These cover difference, union, intersection, and combined operations.
Watch for three common errors. First, do not treat union and intersection as the same operation; union collects everything, intersection keeps only the shared part. Second, do not reverse the order in a difference, because A - B and B - A give different results. Third, convert description form or set-builder form to roster form before you operate.
One pair of sets can show all three operations. With M = {1, 2, 3, 4, 5} and N = {3, 4, 6}: union M \cup N = \{1, 2, 3, 4, 5, 6\}, intersection M \cap N = \{3, 4\}, difference M - N = \{1, 2, 5\}, and N - M = \{6\}.
Once you finish both exercises, browse the full list of Class 6 Maths chapters for the next topic. Check the official CISCE website to confirm the syllabus order for your school year.
Operations on Sets Class 6 ICSE frequently asked questions
How do you find the union of sets class 6 ICSE?
List every element of both sets into one set, writing each element only once. For example, with A = {1, 2, 3} and B = {3, 4}, the union is {1, 2, 3, 4}. The symbol is ∪, so you write A \cup B.
What is the difference between union and intersection of two sets in Class 6 ICSE Maths?
Union gathers every element of both sets, without repeats. Intersection keeps only the elements that appear in both sets at once. For A = {1, 2, 3} and B = {3, 4}, A \cup B = \{1, 2, 3, 4\} but A \cap B = \{3\}.
What does A minus B mean in the difference of two sets in this ICSE chapter?
A - B is the set of elements in A that are not in B. If A = {1, 2, 3} and B = {3, 4}, then A - B = \{1, 2\}. The order matters, because B - A = \{4\}.
Why is the intersection of a set with the empty set always empty in the Class 6 ICSE syllabus?
The empty set contains no elements, so it shares nothing with any other set. The intersection therefore has no elements. That is why A \cap \phi = \phi for every set A.
Do I need to convert a set from description form to roster form before operating in Class 6 ICSE Maths?
Yes. Convert description form or set-builder form to roster form first. For example, “even numbers up to 12” becomes {2, 4, 6, 8, 10, 12}. Then you can find the union, intersection, or difference correctly.
Reference: ICSE Class 6 Mathematics textbook material, chapter 28: Operations on Sets — CISCE-aligned.