Relations and its types concepts are one of the important topics of set theory. Sets, relations and functions all three are interlinked topics. Sets denote the collection of ordered elements whereas relations and functions define the operations performed on sets.
The relations define the connection between the two given sets. Also, there are types of relations stating the connections between the sets. Hence, here we will learn about relations and their types in detail.
Table of Contents
Relations Definition
A relation in mathematics defines the relationship between two different sets of information. If two sets are considered, the relation between them will be established if there is a connection between the elements of two or more non-empty sets.
In the morning assembly at schools, students are supposed to stand in a queue in ascending order of the heights of all the students. This defines an ordered relation between the students and their heights.
Therefore, we can say,
‘A set of ordered pairs is defined as a relation.’
This mapping depicts a relation from set A into set B. A relation from A to B is a subset of A x B. The ordered pairs are (1,c),(2,n),(5,a),(7,n). For defining a relation, we use the notation where,
set {1, 2, 5, 7} represents the domain.
set {a, c, n} represents the range.
Sets and Relations
Sets and relation are interconnected with each other. The relation defines the relation between two given sets.
If there are two sets available, then to check if there is any connection between the two sets, we use relations.
For example, an empty relation denotes none of the elements in the two sets is same.
Let us discuss the other types of relations here.
Relations in Mathematics
In Maths, the relation is the relationship between two or more set of values. Suppose, x and y are two sets of ordered pairs. And set x has relation with set y, then the values of set x are called domain whereas the values of set y are called range. Example: For ordered pairs={(1,2),(-3,4),(5,6),(-7,8),(9,2)} The domain is = {-7,-3,1,5,9} And range is = {2,4,6,8}
Types of Relations
There are 8 main types of relations which include:
Empty Relation
An empty relation (or void relation) is one in which there is no relation between any elements of a set. For example, if set A = {1, 2, 3} then, one of the void relations can be R = {x, y} where, |x – y| = 8. For empty relation,
R = φ ⊂ A × A
Universal Relation
A universal (or full relation) is a type of relation in which every element of a set is related to each other. Consider set A = {a, b, c}. Now one of the universal relations will be R = {x, y} where, |x – y| ≥ 0. For universal relation,
R = A × A
Identity Relation
In an identity relation, every element of a set is related to itself only. For example, in a set A = {a, b, c}, the identity relation will be I = {a, a}, {b, b}, {c, c}. For identity relation,
I = {(a, a), a ∈ A}
Inverse Relation
Inverse relation is seen when a set has elements which are inverse pairs of another set. For example if set A = {(a, b), (c, d)}, then inverse relation will be R-1 = {(b, a), (d, c)}. So, for an inverse relation,
R-1 = {(b, a): (a, b) ∈ R}
Reflexive Relation
In a reflexive relation, every element maps to itself. For example, consider a set A = {1, 2,}. Now an example of reflexive relation will be R = {(1, 1), (2, 2), (1, 2), (2, 1)}. The reflexive relation is given by-
(a, a) ∈ R
Symmetric Relation
In a symmetric relation, if a=b is true then b=a is also true. In other words, a relation R is symmetric only if (b, a) ∈ R is true when (a,b) ∈ R. An example of symmetric relation will be R = {(1, 2), (2, 1)} for a set A = {1, 2}. So, for a symmetric relation,
aRb ⇒ bRa, ∀ a, b ∈ A
Transitive Relation
For transitive relation, if (x, y) ∈ R, (y, z) ∈ R, then (x, z) ∈ R. For a transitive relation,
aRb and bRc ⇒ aRc ∀ a, b, c ∈ A
Equivalence Relation
If a relation is reflexive, symmetric and transitive at the same time, it is known as an equivalence relation.
Representation of Types of Relations
Relation Type
Condition
Empty Relation
R = φ ⊂ A × A
Universal Relation
R = A × A
Identity Relation
I = {(a, a), a ∈ A}
Inverse Relation
R-1 = {(b, a): (a, b) ∈ R}
Reflexive Relation
(a, a) ∈ R
Symmetric Relation
aRb ⇒ bRa, ∀ a, b ∈ A
Transitive Relation
aRb and bRc ⇒ aRc ∀ a, b, c ∈ A
Relation and Function – FAQs
Define Relation and Function.
Relation is defined between two non-empty set A and B such that Relation is a subset of A ⨯ B. Function is defined as a special relation where element of set A is uniquely related to elements of set B.
What is Domain of Relation and Function?
Domain of Relation and Function is the set of input which gives an output when undergoes a relation. Domain can also be considered as pre-image.
What is Range of Relation and Function?
Range of Relation and Function is the set of output obtained when domain undergoes a relation.
What is the Relation between Codomain and Range?
The relation between Codomain and Range is that the Range is a subset of Codomain.
How to Represent Relation and Function?
Relation and Function can be represented using Roaster Form, Set-Builder Form, Arrow Form and Lattice Form. The details have been discussed under the topic above in the article.
What is the Difference between Relation and Function?
The basic difference between Relation and Function is that in Relation pre-image can be unmapped and two or more image can have same pre-image while in case of Function the all the pre-image must have an image and no two or more image can have the same pre-image.
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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".
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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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