CBSE Class 11 Maths Revision Notes Chapter 1 Sets

Sets are well-defined collections of objects, numbers or elements used to organise information in mathematics. For CBSE Class 11 Maths 2026–27, this chapter covers set notation, representation of sets, types of sets, subsets, Venn diagrams and set operations.

Sets is the first chapter in Class 11 Mathematics, but the idea is not new. You already use sets in daily life when you talk about a group of students, a list of subjects, a team of players or a collection of books.

In Maths, a set is a collection with one important rule: it must be clearly defined. This means you should be able to say whether an object belongs to the collection or not.

For example, “vowels in the English alphabet” is a set because the members are fixed: a, e, i, o and u. But “best students in a class” is not a set because different people may choose different students.

Use these CBSE Class 11 Maths Revision Notes Chapter 1 to understand how sets are written, represented and used in operations such as union, intersection, difference and complement.

These Class 11 Maths Chapter 1 Notes also work as CBSE Class 11 Maths Notes Chapter 1 for quick revision of Sets.

Key Takeaways

• Set: A set is a well-defined collection of objects.
• Representation: Sets are represented in roster form and set-builder form.
• Subset: A set A is a subset of B if every element of A is also an element of B.
• Set operations: Union, intersection, difference and complement are the main operations on sets.

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Access Class 11 Maths Chapter 1 Sets Notes in 30 Minutes

These notes are arranged for 30-minute revision, so you can revise the chapter in the same order you study it in class.

Start with the meaning of a set. Then understand how sets are written in roster form and set-builder form. After that, revise types of sets, subsets, Venn diagrams and operations such as union, intersection, difference and complement.

By the end of this chapter, you should be able to look at a collection, decide whether it is a set, represent it correctly and solve basic set operation questions.

These Class 11 Maths Sets Notes and Sets Class 11 Notes cover all important terms, formulas and examples in one place.

Why Do Students Study Sets in Class 11 Maths?

Sets give you the basic language for many Class 11 and Class 12 Maths topics.

You will use the idea of sets in:

So, Sets is not just a separate chapter. It helps you understand how Maths organises information.

These Class 11 Mathematics Revision Notes Chapter 1 help you connect Sets with relations, functions, probability and other higher Maths topics.

Introduction to Sets

The concept of sets is a basic part of modern mathematics.

Sets are used to define relations and functions. They are also used in geometry, probability, sequences, algebra, computer science and other fields.

The theory of sets was developed by German mathematician Georg Cantor while working on problems related to trigonometric series.

What is a Set in Mathematics?

A set is a well-defined collection of objects.

The word “well-defined” is important. It means there should be no confusion about whether something belongs to the set or not.

Example:

A = {1, 2, 3, 4, 5}

This is a set because every element is clearly listed.

Another example:

V = {a, e, i, o, u}

This is the set of vowels in the English alphabet.

Now compare these two collections:

So, in Class 11 Sets, always check one thing first: Can we clearly decide the members?

Set Notation

Once a set is defined, Maths needs symbols to write it quickly. This is where set notation is used.

Sets are usually denoted by capital letters such as A, B, C, X, Y and Z.

Elements are usually denoted by small letters such as a, b, c, x, y and z.

Example:

If A = {2, 4, 6, 8}, then:

2 ∈ A
5 ∉ A
n(A) = 4

Common Sets Used in Class 11 Maths Chapter 1

Examples:

N = {1, 2, 3, 4, 5, ...}

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Representation of Sets

After learning what a set is, the next step is to learn how to write it.

Sets can be represented in two main forms:

Roster Form or Tabular Form

In roster form, all elements of a set are listed inside braces and separated by commas.

Example:

A = {2, 4, 6, 8}

This is the set of even natural numbers less than 10.

Rules of Roster Form

Set-Builder Form

Roster form works well when the set has fewer elements. But when a set is large or follows a rule, set-builder form is easier.

In set-builder form, a set is described using the common property of its elements.

Example:

A = {x : x is an even natural number less than 10}

This means A contains all x such that x is an even natural number less than 10.

So,

A = {2, 4, 6, 8}

Roster Form vs Set-Builder Form

Examples of Representation of Sets

Empty Set

Sometimes, a rule does not give any element. That is when we get an empty set.

An empty set is a set that has no element.

It is also called a null set or void set.

It is denoted by φ or { }.

Examples:

A = {x : x is a natural number between 1 and 2}

There is no natural number between 1 and 2.

So, A = φ.

Another example:

B = {x : x is an even prime number greater than 2}

Since 2 is the only even prime number, B = φ.

Finite and Infinite Sets

A finite set has a definite number of elements.

An infinite set does not have a finite number of elements.

Examples:

Set of days in a week = finite set
Set of natural numbers = infinite set
Set of letters in English alphabet = finite set
Set of points on a line = infinite set

Equal Sets

Two sets A and B are equal if they have exactly the same elements.

Order does not matter.

Repeated elements do not change a set.

Example:

A = {1, 2, 3}
B = {3, 2, 1}

So, A = B.

Another example:

A = {S, C, H, O, O, L}
B = {S, C, H, O, L}

So, A = B because repeated elements are counted only once.

Equivalent Sets

Two sets are equivalent if they have the same number of elements.

They may or may not contain the same elements.

Example:

A = {a, b, c}
B = {1, 2, 3}

Here, n(A) = 3 and n(B) = 3.

So, A and B are equivalent, but not equal.

Subsets

Once you understand sets, the next idea is to compare one set with another.

A set A is a subset of set B if every element of A is also an element of B.

It is written as:

A ⊂ B

Example:

A = {1, 2}
B = {1, 2, 3, 4}

Since every element of A is in B, A ⊂ B.

Important Points on Subsets

Proper Subset

A set A is a proper subset of B if every element of A belongs to B, but A and B are not equal.

Example:

A = {1, 2}
B = {1, 2, 3}

Here, A is a proper subset of B.

Power Set

The power set of a set A is the set of all subsets of A.

It is denoted by P(A).

Example:

If A = {1, 2}, then its subsets are:

φ, {1}, {2}, {1, 2}

So,

P(A) = {φ, {1}, {2}, {1, 2}}

If a set has n elements, then the number of elements in its power set is:

2^n

Example:

If A has 3 elements, then P(A) has 2^3 = 8 elements.

Universal Set

A universal set is the basic set that contains all the elements under discussion.

It is denoted by U.

Example:

If we are studying natural numbers, then U may be the set of natural numbers.

If we are studying vowels, then U may be the set of all letters in the English alphabet.

Subsets of Real Numbers

The set of real numbers has important subsets.

Relations among these sets:

N ⊂ Z ⊂ Q ⊂ R

Also,

T ⊂ R

Irrational numbers are real numbers that are not rational.

Intervals as Subsets of R

Intervals are used to represent subsets of real numbers.

Let a and b be real numbers and a < b.

Example:

{x : x ∈ R, -5 < x ≤ 7} = (-5, 7]

The length of an interval is:

b - a

Venn Diagrams

Set operations become easier when we can see them visually. Venn diagrams help with this.

Venn diagrams are used to show relationships between sets.

They usually contain:

Venn diagrams are useful for understanding union, intersection, difference and complement of sets.

Operations on Sets

Just like numbers have operations such as addition and subtraction, sets also have operations.

Think of two groups in your class.

Set A = students who play cricket
Set B = students who play football

Now:

• A ∪ B means students who play cricket or football or both.
• A ∩ B means students who play both cricket and football.
• A - B means students who play cricket but not football.
• A' means students who do not belong to set A, within the universal set.

This makes set operations easier to understand before using formulas.

Union of Sets

The union of two sets A and B is the set of all elements that belong to A or B or both.

It is written as:

A ∪ B

Example:

A = {1, 2, 3}
B = {3, 4, 5}

A ∪ B = {1, 2, 3, 4, 5}

Common elements are written only once.

Intersection of Sets

The intersection of two sets A and B is the set of all elements common to both A and B.

It is written as:

A ∩ B

Example:

A = {1, 2, 3}
B = {3, 4, 5}

A ∩ B = {3}

Disjoint Sets

Two sets are disjoint if they have no common element.

If A and B are disjoint, then:

A ∩ B = φ

Example:

A = {1, 3, 5}
B = {2, 4, 6}

A ∩ B = φ

So, A and B are disjoint sets.

Difference of Sets

The difference of A and B is the set of elements that belong to A but not to B.

It is written as:

A - B

Example:

A = {1, 2, 3, 4}
B = {3, 4, 5}

A - B = {1, 2}

B - A = {5}

So, A - B and B - A are generally not equal.

Complement of a Set

The complement of set A is the set of all elements in the universal set U that are not in A.

It is written as:

A'

Example:

U = {1, 2, 3, 4, 5, 6}
A = {2, 4, 6}

A' = {1, 3, 5}

Important Laws of Sets

De Morgan’s Laws

De Morgan’s laws are used to simplify expressions involving complements.

These laws are useful in set proofs and Venn diagram questions.

Cardinality of Sets

Cardinality means the number of elements in a set.

It is written as n(A).

Example:

A = {2, 4, 6, 8}

n(A) = 4

Important Formulas for Sets

Formula for Two Sets

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

If A and B are disjoint:

n(A ∪ B) = n(A) + n(B)

Formula 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)

Number of Subsets

If a set A has n elements, then:

Number of subsets = 2^n

Number of proper subsets = 2^n - 1

Solved Examples on Sets

Example 1: Write in Roster Form

Write A = {x : x is a natural number and x < 6} in roster form.

Solution:

Natural numbers less than 6 are 1, 2, 3, 4 and 5.

So,

A = {1, 2, 3, 4, 5}

Example 2: Write in Set-Builder Form

Write {2, 4, 6, 8} in set-builder form.

Solution:

The elements are even natural numbers less than 10.

So,

A = {x : x is an even natural number less than 10}

Example 3: Find Union and Intersection

Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}.

Find A ∪ B and A ∩ B.

Solution:

A ∪ B = {1, 2, 3, 4, 5, 6}

A ∩ B = {3, 4}

Example 4: Find the Complement

Let U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6, 8}.

Find A'.

Solution:

A' contains elements of U that are not in A.

A' = {1, 3, 5, 7}

Example 5: Word Problem on Sets

In a town of 840 people, 450 read Hindi, 300 read English and 200 read both. Find the number of people who read neither.

Solution:

Let H be the set of people who read Hindi.
Let E be the set of people who read English.

n(H) = 450
n(E) = 300
n(H ∩ E) = 200

n(H ∪ E) = n(H) + n(E) - n(H ∩ E)

n(H ∪ E) = 450 + 300 - 200 = 550

People who read neither = Total people - n(H ∪ E)

= 840 - 550

= 290

So, 290 people read neither Hindi nor English.

Quick Highlights of Class 11 Maths Chapter 1 Notes

Important Terms from CBSE Class 11 Maths Revision Notes Chapter 1

The important terms below revise set notation, representation of sets, roster form, set-builder form, empty set, finite set, infinite set, equal sets, equivalent sets, subsets, power set, universal set, Venn diagrams, union of sets, intersection of sets, difference of sets, complement of a set, De Morgan’s laws and cardinality of sets in one place.

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