Sets Class 6 ICSE — Maths Chapter 26
Sets Class 6 ICSE introduces the idea of a set, one of the first building blocks of mathematics. This chapter in the Class 6 ICSE Maths book shows what a set is, what makes it well defined, and how to write one. You will learn the symbols, the properties of sets, and the three ways to represent any collection. By the end, you can convert any set between description, roster, and set builder forms.
Download Idea of a Set Class 6 ICSE Mathematics Chapter 26 PDF
Download the Idea of a Set Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 9 pages, 7 sections, 20 questions.
What is inside Chapter 26
9 pages · 7 sections · 7 worked examples · 20 exercise questions
| Section | Title |
|---|---|
| 26.1 | INTRODUCTION |
| 26.2 | DEFINITION OF A SET |
| 26.3 | WAYS OF REPRESENTING SETS |
| 26.4 | ELEMENTS (or MEMBERS) OF A SET |
| 26.5 | SOME PROPERTIES OF A SET |
| 26.6 | NOTATION (REPRESENTATION) OF A SET |
| 26.7 | SOME IMPORTANT SETS |
- EXERCISE 26(A): 1 questions
- EXERCISE 26(B): 6 questions
- EXERCISE 26(C): 5 questions
- Revision Exercise (Chapter 26): 8 questions
26.1 INTRODUCTION
Every day, people talk about collections without calling them sets. A person who saves stamps has a collection of stamps. A child with many toys has a collection of toys. A student carrying books has a collection of books. Groups work the same way. A group of boys playing hockey, a group of girls playing badminton, or a group of students going for a picnic are all collections.
In mathematics, a collection of particular things or a group of particular objects is called a set. The word “particular” matters here. A set is not any random pile of things. It is a defined group of objects, gathered for a purpose. The chapter makes this point before it gives the formal definition.
This chapter of the Class 6 ICSE syllabus builds from this simple idea. Each section adds one piece: what makes a set valid, how to write it, how to name its parts, and how to use the standard notation. You can check the complete curriculum on the CISCE board site.
26.2 DEFINITION OF A SET
A set is a collection of well-defined objects. The phrase “well-defined” carries the whole idea. It must be absolutely clear which object belongs to the set and which does not. If two people can disagree about what belongs, the collection is not a set.
The chapter uses simple examples. “Lovely flowers” is not a set. Lovely is a relative term; what one person calls lovely, another may not. “Red flowers” is a set, because every red flower clearly belongs. “Young players” is not a set, because no age range is given. “Players aged between 14 and 18 years” is a set, because the range decides inclusion exactly.
Worked pattern: Test “tasty fruits”. Tasty is a judgement, not a fact, so the collection is not a set. Now test “fruits heavier than 200 grams”. Every fruit can be weighed and compared with certainty, so this collection is a set. The test is always the same: can anyone say with certainty whether a given object belongs?
26.3 WAYS OF REPRESENTING SETS
The chapter shows two ways to display a set. The first is visual: draw the objects as pictures inside a closed figure, such as a circle, a rectangle, or a square. A set of fruits appears as drawings of a banana, apple, grapes, and mango inside a circle. A set of sports goods appears as a cricket bat, tennis racket, football, and hockey inside a square. The closed figure keeps the set together visually.
The second way is faster and more convenient: write the names of the objects inside a pair of curly braces. The same fruit set becomes { banana, apple, grapes, mango }. The sports set becomes { cricket bat, tennis racket, football, hockey }. The braces work like the closed figure in the drawing. They mark the boundary of the set.
Writing names inside curly braces saves time and space. Drawing pictures takes effort, especially for large sets. Names in braces are quick to write and easy to read. For the rest of this ICSE chapter, this brace notation is the standard. Every later section uses it.
26.4 ELEMENTS (or MEMBERS) OF A SET
The objects that form a set are called its elements or members. The elements sit inside a pair of curly braces, separated by commas. The name of the set is always a capital letter.
For example, A = \{ p, q, r, s, t \}. Here A is the set name, and p, q, r, s, t are its elements.
The chapter introduces two symbols. The Greek letter epsilon, written \in, means “belongs to” or “is an element of”. The crossed version, \notin, means “does not belong to” or “is not an element of”. So p \in A reads “p belongs to set A”. The statement a \notin A reads “a does not belong to set A”.
Worked pattern: Let set A = \{ 4, 8, 12, 16, 20 \}. Test three statements.
- 8 \in A is true, because 8 appears in the list.
- 12 \notin A is false, because 12 does appear.
- 16 \in A is true, because 16 appears.
The rule: check the list, nothing more.
26.5 SOME PROPERTIES OF A SET
Two properties of a set matter throughout the chapter.
Property 1: order does not matter. Changing the order of elements does not change the set. The set \{ 5, 6, 7, 8 \} is the same as \{ 6, 8, 7, 5 \}. Both contain exactly 5, 6, 7, and 8.
Property 2: repetition does not matter. Repeating an element does not change the set. The set \{ a, b, d, a, c, b \} equals \{ a, b, c, d \}. Each element is written only once, even if it appeared several times.
These properties change how you write sets from words. The set of letters in “book” is \{ b, o, k \}, because the double o is written once. The set of letters in “PUPPET” is \{ p, u, e, t \}, because p and t each appear twice.
Review rules: elements go inside curly braces separated by commas; the set name is a capital letter; alphabet elements are small letters; any order is allowed; no element is repeated.
Worked pattern: Write the set of letters in “MUSSORIE”. The distinct letters are m, u, s, o, r, i, e. So the set is \{ m, u, s, o, r, i, e \}. The double s is written once.
Students often slip on these two properties. The table below lists the common mistakes and how to avoid them.
| Mistake | Correct rule | How to check |
|---|---|---|
| Writing \{5, 5, 5\} with repeats | Write each element once | Count each distinct element once |
| Saying \{1, 2, 3\} differs from \{3, 2, 1\} | Order does not change a set | Compare the distinct elements |
| Using a small letter for the set name | Set names are capital letters | Check the first character |
| Listing elements without commas | Separate elements with commas | Look for commas between entries |
26.6 NOTATION (REPRESENTATION) OF A SET
The chapter presents three methods for writing a set. Each method shows the same set in a different way.
Description method: give a well-defined description of the elements, often enclosed in curly brackets. Example: { numbers greater than 40 and smaller than 75 }.
Roster or tabular method: list the elements inside curly braces, separated by commas. Example: Q = \{ 1, 2, 3, 4, 5 \}.
Rule or set-builder method: give a rule or formula instead of listing elements. Example: A = \{ x : x \text{ is a counting number greater than 12} \}. The symbol : or | reads “such that”. So the expression reads “A is the set of elements x such that x is a counting number greater than 12”.
Here is the same set in all three forms.
| Method | Form |
|---|---|
| Description | The set of counting numbers between 10 and 20 |
| Roster | \{ 11, 12, 13, 14, 15, 16, 17, 18, 19 \} |
| Set-builder | \{ x : x \text{ is a counting number between 10 and 20} \} |
Worked pattern: Convert “the set of counting numbers between 10 and 20” through all three forms. The description is given. The roster lists every number from 11 to 19, since 10 and 20 are excluded. The set-builder form writes the rule with the variable x and the “such that” symbol. The same set appears three different ways.
These three methods are used throughout the Class 6 ICSE Maths book. Every set you meet from here on will use one of these forms.
26.7 SOME IMPORTANT SETS
Five standard number sets appear so often that they get fixed names and symbols. The chapter gives all three forms for each.
| Set | Symbol | Roster form |
|---|---|---|
| Natural numbers | N | \{ 1, 2, 3, 4, \ldots \} |
| Whole numbers | W | \{ 0, 1, 2, 3, 4, 5, \ldots \} |
| Integers | Z or I | \{ \ldots, -3, -2, -1, 0, 1, 2, 3, \ldots \} |
| Even natural numbers | E | \{ 2, 4, 6, 8, \ldots \} |
| Odd natural numbers | O | \{ 1, 3, 5, 7, 9, \ldots \} |
Almost every set can be written in all three forms. Take the set of odd natural numbers less than 15. In description form: “set of odd natural numbers less than 15”. In roster form: \{ 1, 3, 5, 7, 9, 11, 13 \}. In set-builder form: \{ x : x \text{ is an odd natural number less than 15} \}.
Mnemonic: New Whole Integers Even Odd. The first letter of each word matches N, W, I, E, O. Each set adds one layer: N starts at 1, W adds 0, I adds negatives, E keeps the even numbers, O keeps the odd ones.
What to practise from Sets Class 6 ICSE
Four exercise blocks test this chapter. Practise each after finishing the section it covers.
- EXERCISE 26(A) — 1 question on well-defined sets. Do this after section 26.2.
- EXERCISE 26(B) — 6 questions on elements, the \in and \notin symbols, and set properties. Do this after sections 26.4 and 26.5.
- EXERCISE 26(C) — 5 questions on roster and set-builder forms. Do this after section 26.6.
- Revision Exercise (Chapter 26) — 8 questions covering the whole chapter. Do this last.
This order builds each skill before the next one needs it. The next chapter in this book continues with types of sets, which builds directly on what you practise here.
Sets Class 6 ICSE frequently asked questions
What does the symbol ∈ mean in sets class 6 ICSE?
The symbol \in (Greek epsilon) means “belongs to” or “is an element of”. If p \in A, read it as “p belongs to set A”. The crossed version \notin means the opposite: “does not belong to”.
When is a collection not a set in Class 6 maths?
A collection is not a set when its objects are not well-defined. That happens when a word is a judgement, like “lovely” or “young”, or when no clear rule decides what belongs. If two people can disagree about membership, the collection is not a set.
What is the difference between roster form and set builder form in Class 6 ICSE?
Roster form lists every element inside curly braces, like \{ 1, 2, 3, 4, 5 \}. Set-builder form gives a rule instead of a list, like \{ x : x \text{ is a counting number less than 6} \}. Roster shows the elements; set-builder shows the condition.
Why is the set {5, 5, 5} the same as {5} in sets class 6 ICSE?
Because repetition does not change a set. The property says a set remains the same even if elements repeat. So \{ 5, 5, 5 \} and \{ 5 \} both contain the single element 5. Write the element once.
How do I write the set of letters in a word like PUPPET in Class 6 ICSE?
List each distinct letter once, ignoring repeats. PUPPET has the letters p, u, e, t, since p appears twice and t appears twice. The set is \{ p, u, e, t \}.
Reference: ICSE Class 6 Mathematics textbook material, chapter 26: Idea of a Set — CISCE-aligned.