Sets Class 6 ICSE — Chapter 27 Types of Sets
Sets class 6 ICSE Maths introduces the different kinds of sets you will use throughout Mathematics. This chapter covers finite, infinite, empty, equal, equivalent, disjoint and overlapping sets. Each section answers one question about a set: can you count its elements, is it empty, are two sets identical, do they match in count, or do they share elements? By the end you can name any set correctly and tell two sets apart.
Download Types of Sets Class 6 ICSE Mathematics Chapter 27 PDF
Download the Types of Sets Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 5 pages, 7 sections, 15 questions.
What is inside Chapter 27
5 pages · 7 sections · 1 worked examples · 15 exercise questions
| Section | Title |
|---|---|
| 27.1 | INTRODUCTION |
| 27.2 | FINITE SET |
| 27.3 | INFINITE SET |
| 27.4 | THE EMPTY SET or THE NULL SET |
| 27.5 | EQUAL SETS |
| 27.6 | EQUIVALENT SETS |
| 27.7 | DISJOINT SETS |
- EXERCISE 27: 9 questions
- Revision Exercise (Chapter 27): 6 questions
27.1 INTRODUCTION
The introduction poses five questions about any set you are given. Each question leads to one set type explained later in this chapter. The five questions are listed below.
Can the elements of a set be counted? That separates finite sets from infinite sets. Is a set empty? That is the empty set. Do two sets have identical elements? Those are equal sets. Do two sets have the same number of elements? Those are equivalent sets. Do two sets share any elements? That decides whether they are disjoint or overlapping sets.
Every later section in this ICSE chapter answers exactly one of these five questions. Work through them in order and each set type becomes easy to recognise. You first met a set in the previous chapter on the idea of a set. That chapter defines a set and shows how to write one in roster form. The questions in this introduction are the key to telling the set types apart.
27.2 FINITE SET
A finite set has a limited number of elements. You can count every element one by one. A school roll is finite because each student can be listed. The days in a year form a finite set too. The set of whole numbers between 10 and 20 is also finite. Any set you can finish counting is finite.
Roster form lists the elements of a finite set. When the list is long, a pattern with dots is used. For natural numbers less than 100, write:
P = \{1, 2, 3, \dots, 99\}
The dots mean the pattern continues up to 99, then stops. Every element in P can be counted. That is what makes P a finite set. The key test is simple: if you can count the elements, the set is finite. Even a very large set stays finite as long as the count ends somewhere.
27.3 INFINITE SET
An infinite set has an unlimited number of elements. You cannot finish counting them. The set of whole numbers is infinite. The set of stars in the sky is infinite for the same reason. No matter how far you count, more elements remain.
Roster form shows a few elements of an infinite set, then dots. The dots mean the pattern continues without end. For multiples of 5, write \{5, 10, 15, \dots\}. There is no last multiple of 5.
The natural numbers greater than 32 follow the same idea. Write \{33, 34, 35, 36, \dots\} to show the pattern. A common error is to read the dots as a stop. In an infinite set, the dots mean the list never ends. Compare this with the finite set in section 27.2, where the dots stop at a final element.
27.4 THE EMPTY SET or THE NULL SET
The empty set has no elements. It is written as \{\} or as \emptyset. Both symbols name the same set. The Greek letter \emptyset, read as phi, is another way to show an empty set.
For example, let B = \{\text{even numbers not divisible by 2}\}. No even number fails to divide by 2. So B has no elements and B = \emptyset. Another example is the set of triangles with five sides, which also has no members.
A common mistake is to confuse \{0\} with the empty set. The set \{0\} contains one element: the number zero. It is not empty. The empty set contains nothing at all.
The empty set is a finite set. You can count its elements. The count is zero, and zero is a countable number.
27.5 EQUAL SETS
Two sets are equal when their elements are identical. Every element of the first set appears in the second set. Every element of the second set appears in the first set. The symbol used is the usual equals sign.
For example, let C = \{a, e, i, o, u\} and D = \{\text{vowels in the English alphabet}\}. Both sets contain the same five letters. So C = D.
Order does not matter. The set \{3, 5, 7\} equals the set \{7, 3, 5\}. Repeating an element does not change the set either. The set \{1, 1, 2, 2\} equals the set \{1, 2\}. Only the distinct elements decide equality.
27.6 EQUIVALENT SETS
Two sets are equivalent when they have the same number of elements. The elements themselves may differ. Only the count matters.
For example, let A = \{2, 4, 6, 8\} and B = \{a, b, c, d\}. Set A has four elements. Set B has four elements too. So A and B are equivalent sets, even though their elements are completely different.
Here is a worked example that separates the two ideas. Let X = \{1, 3, 5\} and Y = \{5, 3, 1\}. Both sets contain exactly 1, 3 and 5. So X and Y are equal sets. They are also equivalent, since both have three elements.
Now let P = \{1, 3, 5\} and Q = \{2, 4, 6\}. Both have three elements, so P and Q are equivalent. But the elements differ, so P and Q are not equal. Equal sets are always equivalent. The converse is not always true.
Two more rules follow from the same idea. Two empty sets are always equal. Two infinite sets are always equivalent.
27.7 DISJOINT SETS
Two sets are disjoint when they have no element in common. Two sets are overlapping, also called joint sets, when they share at least one element. The comparison table below shows every set type at a glance.
Let P = \{2, 4, 6, 8, 10\} and Q = \{3, 6, 9, 12\}. Both sets contain 6. So P and Q are overlapping sets. Now let R = \{1, 2\} and S = \{7, 8, 9\}. No element appears in both sets. So R and S are disjoint sets.
The letter D in disjoint is a memory aid. D means different elements. If even one element is shared, the sets overlap instead.
| Set type | What makes it that type | Quick example |
|---|---|---|
| Finite | countable elements | \{1, 2, 3, \dots, 99\} |
| Infinite | uncountable elements | \{5, 10, 15, \dots\} |
| Empty | no elements | \{\} = \emptyset |
| Equal | identical elements | \{3, 5, 7\} = \{7, 3, 5\} |
| Equivalent | same count | \{2, 4, 6, 8\} and \{a, b, c, d\} |
| Disjoint | no common element | \{1, 2\} and \{7, 8, 9\} |
| Overlapping | at least one common element | \{2, 4, 6\} and \{3, 6, 9\} |
What to practise from Sets Class 6 ICSE
The chapter has two exercise blocks. EXERCISE 27 has 9 questions. Revision Exercise (Chapter 27) has 6 questions. Both blocks train the same set types covered in this ICSE chapter.
| Questions | Skill practised |
|---|---|
| Exercise 27 Q1, Q4, Q7 | Finite or infinite |
| Exercise 27 Q2, Q5 | Empty set |
| Exercise 27 Q3, Q6 | Equal versus equivalent |
| Exercise 27 Q8 | True or False |
| Exercise 27 Q9 | Disjoint or overlapping |
| Revision Q1–Q3 | Give examples from surroundings |
| Revision Q4 | Classify as empty, finite, infinite |
| Revision Q5 | Disjoint or overlapping |
| Revision Q6 | Identify empty sets |
Work through each question group in order. The question styles in these exercises prepare you for the kinds of set questions that appear in the board examination. The official CISCE board syllabus lists the same set types for Class 6 Mathematics. You can also browse all the Class 6 Maths chapters on this site to see what comes after sets.
Sets Class 6 ICSE frequently asked questions
What is the difference between equal sets and equivalent sets in sets class 6 icse?
Equal sets have identical elements. Equivalent sets have the same number of elements, but the elements may differ. Every pair of equal sets is equivalent. Two equivalent sets are not always equal.
Is {0} the same as the empty set?
No. The set \{0\} contains one element, the number zero. The empty set contains no elements at all. It is written as \{\} or \emptyset.
How do I tell if a set is finite or infinite?
Try to count the elements. If the count finishes, the set is finite. If the elements keep going without end, the set is infinite. Look at the dots in roster form. Dots with a last element mean finite. Dots without a stop mean infinite.
When are two sets disjoint and when are they overlapping?
Two sets are disjoint when they share no element. Two sets are overlapping, or joint, when they share at least one element. Check for common elements to decide.
Why is the empty set called a finite set?
The empty set has zero elements. Zero is a countable number. So the empty set counts as a finite set.
Reference: ICSE Class 6 Mathematics textbook material, chapter 27: Types of Sets — CISCE-aligned.