Types Of Sets-Empty Set, Non-Empty Set, Finite Set, Infinite Set, Singleton Set, Equivalent Set, Subset, Superset, Power Set, Universal Set | Class 11 Math Notes Study Material Download Free PDF

Example: Separate out the collections that can be placed in a set.

  • Beautiful Girls in a class
  • All even numbers
  • Good basketball players
  • Natural numbers divisible by 3
  • Number from 1 to 10

Answer:

Anything that tries to define a certain quality or characteristics can not be put in a set. Hence, from the above given Collection of data. 

The ones that can be a set,

  • All even numbers
  • Natural numbers divisible by 3.
  • Number from 1 to 10

The ones that cannot be a set,

  • Beautiful girls in the park
  • Good basketball players

Types of Sets in Mathematics

Sets are the collection of different elements belonging to the same category and there can be different types of sets seen. A set may have an infinite number of elements, may have no elements at all, may have some elements, may have just one element, and so on. Based on all these different ways, sets are classified into different types.

The different types of sets are:

Singleton SetEmpty Set
Finite SetInfinite Set
Equal SetEquivalent Set
SubsetPower Set
Universal Set Disjoint Sets

Let’s discuss these various types of sets in detail.

Singleton Set

Singleton Sets are those sets that have only 1 element present in them.

Example: 

  • Set A= {1} is a singleton set as it has only one element, that is, 1.
  • Set P = {a : a is an even prime number} is a singleton set as it has only one element 2.

Similarly, all the sets that contain only one element are known as Singleton sets.

Empty Set

Empty sets are also known as Null sets or Void sets. They are the sets with no element/elements in them. They are denoted as ϕ.

Example:

  • Set A= {a: a is a number greater than 5 and less than 3}
  • Set B= {p: p are the students studying in class 7 and class 8}

Finite Set

Finite Sets are those which have a finite number of elements present, no matter how much they’re increasing number, as long as they are finite in nature, They will be called a Finite set.

Example: 

  • Set A= {a: a is the whole number less than 20}
  • Set B = {a, b, c, d, e}

Infinite Set

Infinite Sets are those that have an infinite number of elements present, cases in which the number of elements is hard to determine are known as infinite sets. 

Example: 

  • Set A= {a: a is an odd number}
  • Set B = {2,4,6,8,10,12,14,…..}

Equal Set

Two sets having the same elements and an equal number of elements are called equal sets. The elements in the set may be rearranged, or they may be repeated, but they will still be equal sets.

Example:

  • Set A = {1, 2, 6, 5}
  • Set B = {2, 1, 5, 6}

In the above example, the elements are 1, 2, 5, 6. Therefore, A= B.

Equivalent Set

Equivalent Sets are those which have the same number of elements present in them. It is important to note that the elements may be different in both sets but the number of elements present is equal. For Instance, if a set has 6 elements in it, and the other set also has 6 elements present, they are equivalent sets.

Example:

Set A= {2, 3, 5, 7, 11}

Set B = {p, q, r, s, t}

Set A and Set B both have 5 elements hence, both are equivalent sets.

Subset

Set A will be called the Subset of Set B if all the elements present in Set A already belong to Set B. The symbol used for the subset is 

If A is a Subset of B, It will be written as A ⊆ B

Example:

Set A= {33, 66, 99}

Set B = {22, 11, 33, 99, 66}

Then, Set A ⊆ Set B 

Power Set

Power set of any set A is defined as the set containing all the subsets of set A. It is denoted by the symbol P(A) and read as Power set of A.

For any set A containing n elements, the total number of subsets formed is 2n. Thus, the power set of A, P(A) has 2n elements.

Example: For any set A = {a,b,c}, the power set of A is?

Solution:

Power Set P(A) is,

P(A) = {ϕ, {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}}

Universal Set 

A universal set is a set that contains all the elements of the rest of the sets. It can be said that all the sets are the subsets of Universal sets. The universal set is denoted as U.

Example: For Set A = {a, b, c, d} and Set B = {1,2} find the universal set containing both sets.

Solution:

Universal Set U is,

U = {a, b, c, d, e, 1, 2}

Disjoint Sets

For any two sets A and B which do have no common elements are called Disjoint Sets. The intersection of the Disjoint set is ϕ, now for set A and set B A∩B =  ϕ. 

Example: Check whether Set A ={a, b, c, d} and Set B= {1,2} are disjoint or not.

Solution:

Set A ={a, b, c, d}
Set B= {1,2}

Here, A∩B =  ϕ

Thus, Set A and Set B are disjoint sets.

Summarizing Types of Set

There are different types of sets categorized on various parameters. Some types of sets are mentioned below:

Set NameDescriptionExample
Empty SetA set containing no elements whatsoever.{}
Singleton SetA set containing exactly one element.{1}
Finite SetA set with a limited, countable number of elements.{apple, banana, orange}
Infinite SetA set with an uncountable number of elements.{natural numbers (1, 2, 3, …)}
Equivalent SetsSets that have the same number of elements and their elements can be paired one-to-one.Set A = {1, 2, 3} and Set B = {a, b, c} (assuming a corresponds to 1, b to 2, and c to 3)
Equal SetsSets that contain exactly the same elements.Set A = {1, 2} and Set B = {1, 2}
Universal SetA set containing all elements relevant to a specific discussion.The set of all students in a school (when discussing student grades)
Unequal SetsSets that do not have all the same elements.Set A = {1, 2, 3} and Set B = {a, b}
Power SetThe set contains all possible subsets of a given set.Power Set of {a, b} = { {}, {a}, {b}, {a, b} }
Overlapping SetsSets that share at least one common element.Set A = {1, 2, 3} and Set B = {2, 4, 5}
Disjoint SetsSets that have no elements in common.Set A = {1, 2, 3} and Set B = {a, b, c}
SubsetA set where all elements are also members of another set.{1, 2} is a subset of {1, 2, 3}

Solved Examples on Types of Sets

Example 1: Represent a universal set on a Venn Diagram.

Solution:

Universal Sets are those that contain all the sets in it. In the below given Venn diagram, Set A and B are given as examples for better understanding of Venn Diagram.

Example:

Set A= {1,2,3,4,5}, Set B = {1,2, 5, 0}

U= {0, 1, 2, 3, 4, 5, 6, 7}

Universal Set

Example 2: Which of the given below sets are equal and which are equivalent in nature?

  • Set A= {2, 4, 6, 8, 10}
  • Set B= {a, b, c, d, e}
  • Set C= {c: c ∈ N, c is an even number, c ≤ 10}
  • Set D = {1, 2, 5, 10}
  • Set E= {x, y, z}

Solution:

Equivalent sets are those which have the equal number of elements, whereas, Equal sets are those which have the equal number of elements present as well as the elements are same in the set.

Equivalent Sets = Set A, Set B, Set C.

Equal Sets = Set A, Set C.

Example 3: Determine the types of the below-given sets,

  •  Set A= {a: a is the number divisible by 10}
  • Set B = {2, 4, 6}
  • Set C = {p}
  • Set D= {n, m, o, p}
  • Set E= ϕ

Solution:

From the knowledge gained above in the article, the above-mentioned sets can easily be identified.

  • Set A is an Infinite set.
  • Set B is a Finite set
  • Set C is a singleton set
  • Set D is a Finite set
  • Set E is a Null set

Example 4: Explain which of the following sets are subsets of Set P,

Set P = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

  • Set A = {a, 1, 0, 2}
  • Set B ={0, 2, 4}
  • Set C = {1, 4, 6, 10}
  • Set D = {2, 20}
  • Set E ={18, 16, 2, 10}

Solution:

  • Set A has elements a, 1, which are not present in the Set P. Therefore, set A is not a Subset.
  • Set B has elements which are present in set P, Therefore, Set B ⊆ Set P
  • Set C has 1 as an extra element. Hence, not a subset of P
  • Set D has 2, 20 as element. Therefore, Set D ⊆ Set P
  • Set E has all its elements matching the elements of set P. Hence, Set E ⊆ Set P.

FAQs on Types of Sets

What are sets?

Sets are well-defined collections of objects. 

Example: The collection of Tata cars in the parking lot is a set.

What are Sub Sets?

Subsets of any set are defined as sets that contain some elements of the given set. For example, If set A contains some elements of set B set A is called the subset of set B.

How many types of sets are present?

Different types of sets used in mathematics are 

  • Empty Set
  • Non-Empty Set
  • Finite Set
  • Infinite Set
  • Singleton Set
  • Equivalent Set
  • Subset
  • Superset
  • Power Set
  • Universal Set

What is the difference between, ϕ and {ϕ}?

The difference between ϕ and {ϕ} is

  • ϕ = this symbol is used to represent the null set, therefore, when only this symbol is given, the set is a Null set or empty set.
  • {ϕ}= In this case, the symbol is present inside the brackets used to denote a set, and therefore, now the symbol is acting like an element. Hence, this is a Singleton set.

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.

CBSE Class 11 Maths Syllabus for 2023-24 with Marking Scheme

CBSE syllabus for class 11 Maths is divided into 5 units. The table below shows the units, number of periods and marks allocated for maths subject. The maths theory paper is of 80 marks and the internal assessment is of 20 marks.

No.UnitsMarks
I.Sets and Functions23
II.Algebra25
III.Coordinate Geometry12
IV.Calculus08
V.Statistics and Probability12
Total Theory80
Internal Assessment20
Grand Total100

2025-26 CBSE Class 11 Maths Syllabus

Below you will find the CBSE Class Maths Syllabus for students.

Unit-I: Sets and Functions

1. Sets

Sets and their representations, empty sets, finite and infinite sets, equal sets, subsets, and subsets of a set of real numbers, especially intervals (with notations), universal set, Venn diagrams, union and intersection of sets, difference of sets, complement of a set and properties of complement.

2. Relations & Functions

Ordered pairs, Cartesian product of sets, number of elements in the Cartesian product of two finite sets, Cartesian product of the set of reals with itself (upto R x R x R), definition of relation, pictorial diagrams, domain, co-domain and range of a relation. Function as a special type of relation. Pictorial representation of a function, domain, co-domain and range of a function. Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatest integer functions, with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions

Positive and negative angles, measuring angles in radians and in degrees and conversion from one measure to another, definition of trigonometric functions with the help of unit circle, truth of the identity, signs of trigonometric functions, domain and range of trigonometric functions and their graphs, expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple applications.

Unit-II: Algebra

1. Complex Numbers and Quadratic Equations

Need for complex numbers, especially√−1, to be motivated by the inability to solve some of the quadratic equations. Algebraic properties of complex numbers, Argand plane.

2. Linear Inequalities

Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line.

3. Permutations and Combinations

The fundamental principle of counting. Factorial n. (n!) Permutations and combinations, derivation of Formulae for nPr and nCr and their connections, simple applications.

4. Binomial Theorem

Historical perspective, statement and proof of the binomial theorem for positive integral indices, Pascal’s triangle, simple applications.

5. Sequence and Series

Sequence and series, arithmetic progression (A. P.), arithmetic mean (A.M.),  geometric progression (G.P.), general term of a G.P., sum of n terms of a G.P., infinite G.P. and its sum, geometric mean (G.M.), relation between A.M. and G.M.

Unit-III: Coordinate Geometry

1. Straight Lines

Brief recall of two-dimensional geometry from earlier classes. Slope of a line and angle between two lines. Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form. General equation of a line. Distance of a point from a line.

2. Conic Sections

Sections of a cone: circles, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola. Standard equation of a circle.

3. Introduction to Three-Dimensional Geometry

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points.

Unit-IV: Calculus

1. Limits and Derivatives

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit, limits of polynomials and rational functions trigonometric, exponential and logarithmic functions, definition of derivative relate it to the slope of the tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

Unit-V: Statistics and Probability

1. Statistics

Measures of Dispersion: Range, mean deviation, variance and standard deviation of ungrouped/grouped data.

2. Probability

Events; occurrence of events, ‘not’, ‘and’ and ‘or’ events, exhaustive events, mutually exclusive events, Axiomatic (set theoretic) probability, connections with other theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ and ‘or’ events.

Students can also get the syllabus of all the subjects by visiting CBSE Class 11 Syllabus page. Learn Maths & Science in an interactive & fun-loving way with Anand Classes App/Tablet.

Frequently Asked Questions on CBSE Class 11 Maths Syllabus 2025-26

Q1

What is the marks distribution for internals and theory exams according to the CBSE Maths Syllabus for Class 11?

The marks distribution for internals is 20 marks and the theory exam is 80 marks based on the CBSE Class 11 Maths Syllabus.

Q2

Which is the most important chapter in the CBSE Class 11 Maths Syllabus?

The important chapter in the CBSE Class 11 Maths Syllabus is Algebra which is for 25 marks in the overall weightage.

Q3

What are the chapters covered in Unit III of the CBSE Class 11 Maths Syllabus?

The chapters covered in Unit III of the CBSE Class 11 Maths Syllabus are straight lines, conic sections and an introduction to three-dimensional geometry.