Universal Set is a set that has all the elements associated with a given set, without any repetition. Suppose we have two sets P = {1, 3, 5} and Q = {2, 4, 6} then the universal set of P and Q is U = {1, 2, 3, 4, 5, 6}. We generally use U to denote universal sets.
Universal Set is a type of set that is used to represent all the possible elements associated with a set. It is widely used in probability to represent all possible sample space of an event. In this article, we will learn about, Universal sets, Examples of Universal Sets, Complements of Universal Sets, Venn Diagram of Universal Sets, and others in detail.
Table of Contents
Universal Set Definition
Universal Set is the set of all the sets, i.e., it contains all the elements present in all the sets given. The universal set is represented as U, and it is represented as a rectangle in the Venn diagram, all the other sets are drawn inside the rectangle, this is done to show that the universal set contains all the possible elements of all the sets.
Assume set A and set B,
Set A = {1, 2, 3, 4}
Set B= {2, 4, 5, 6, 7, 8}
Then the universal set containing set A and set B is, U and is defined as,
U= {1, 2, 3, 4, 5, 6, 7, 8}
We also define that set of complex number is the universal set of the number because it contains all the numbers including, Imaginary Numbers, Real Numbers, Rational Numbers, Irrational Numbers, Integers, Whole Numbers, Natural Numbers, etc.
Universal Sets Symbol
We use English Letter ‘U‘ for representing Universal Set. It contain all the elements associate with the concerning sets.
Universal Sets Examples
Examples of universal set are,
Set of Complex Number is the universal set of all the numbers as it contains all the numbers.
Suppose we have three sets,
Set A = (Alphabets in Government)
Set B = {a, e, i, o, u}
Set C = (Alphabets in Country)
Then the universal set of set A, set B, and set C is,
U = (All alphabets in English Language)
Complements of Universal Sets
We know that universal set U is a set that contains all the elements of subsets, so compelement of the universal set is a set that contain no elements of the subsets. Thus, we can say that, the complement of the universal set is an Empty Set Or Null Set. A null set is denoted by ‘{}’ or ‘Φ’ symbol.
Venn Diagram of Universal Set
Venn Diagrams are used to represent relation between sets using pictorials methods. We use circles to represent various sets. A universal set is a set that contains all the elements associated with all the sets in considerations. We use rectangles to represents Universal Sets.
The image added below shows the universal set U which contains three sets A, B and C. The region of intersection of sets is also shown.
Difference Between Universal Set and Union of Sets
Universal set is a set that contain all the elements associated with the subset in concern (it can also have more elements that are not prsesnt in the subsets), where as union of two sets only contain the elements that are present in the two sets any extra elements is not allowed in the union of to sets.
The basic differences between Universal Set and Union of Sets can be understood with the table added below:
Universal Set
Union of Sets
A set containing all the elements associated with the concerning set is called the universal set.
A set containing elements that are present in the sets whose union is to be taken is called the union of set.
Universal set is denoted using letter “U”
Union of two sets is an operation and is denoted using union operator ‘∪’. Suppose we have to find union of set A and set B then, it is represented as,A∪B and is read as A union B
Universal set can contain some extra elements other than the elements in the subset.
Union of a set can not have more than elements that are in the subset.
Example,Set A = {1, 3, 5, 7}Set B = {2, 4, 6, 8}Universal Set ‘U’U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
Example,Set A = {1, 3, 5, 7}Set B = {2, 4, 6, 8}Union of set A and set BA ∪ B = { 1, 2, 3, 4, 5, 6, 7, 8}
Solved Examples on Universal Sets
Problem 1: Represent the information given below in Venn diagram,
Set A = {1, 3, 5}
Set B = {5, 7, 9}
U = {1, 3, 5, 6, 7, 9,11, 13, 15}
Solution:
Given set,
Set A = {1, 3, 5}
Set B= {5, 7, 9}
U = {1, 3, 5, 6, 7, 9,11, 13, 15}
Universal set “U” is represented as,
Problem 2: Find the universal set of
set A = {3, 6, 9, 12}
set B = {1, 2, 3, 4, 5}
Solution:
Given set,
Set A = {1, 3, 5}
Set B= {5, 7, 9}
Universal set ‘U’
U = {1, 2, 3, 4, 5, 6, 9, 12}
FAQs on Universal Sets
What is a Set?
A set is a well defined collection of distinct objects. It is a concept in mathematics that is used to represent various various group of things. For example suposse in a class a group of students having 150 cm height is a set.
What is a Universal Set?
Universal set is a set that contains all the elements of the sets associated with the given set. A universal set contains all the elements of the sets.
What is Union of a Set?
Union of a set is a set that contain all the elements of the sets that union has to be calculated. Suppose we have a set A = {1, 2, 3, 4} and set B = {3, 4, 5, 6} than the union of A and B is A ∪ B and its value is, A ∪ B = {1, 2, 3, 4, 5, 6}
What is Superset?
A set that contains all the elements of the other set is called the superset of the first set. Suppose we have a set A and set B and if all the elements of set A are contained in set B then set B is called the superset of set A and is represented as, A ⊇ B.
How is Universal Set Represented?
A universal set is represented using the English alphabet ‘U’.
Neeraj Anand, Param Anand
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.
Units
Marks
I.
Sets and Functions
23
II.
Algebra
25
III.
Coordinate Geometry
12
IV.
Calculus
08
V.
Statistics and Probability
12
Total Theory
80
Internal Assessment
20
Grand Total
100
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.
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