Relations

Complete Class 11 Relations chapter with ordered pairs, Cartesian product, definition of relations, types of relations, domain, codomain, range, and applications.

1.Introduction to Relations
Meaning of a relation, how relations come from sets, and simple examples using ordered pairs.
2.Ordered Pairs
Meaning of ordered pairs, why order matters, and simple examples showing how pairs represent connections.
3.Cartesian Product of Sets
Meaning of Cartesian product, how it forms ordered pairs from two sets, with notation and simple examples.
4.Properties of Cartesian Products
Key properties of Cartesian products including order, empty set behavior, subsets, and simple examples.
5.Definition of a Relation
Meaning of a relation, how it is formed from the Cartesian product, and simple examples using ordered pairs.
6.Representation of Relations
Different ways to represent a relation using ordered pairs, arrow diagrams, tables, and set-builder form.
7.Domain, Codomain & Range of a Relation
Meaning of domain, codomain, and range of a relation with simple explanations and examples.
8.Types of Relations (Overview)
Overview of different types of relations including reflexive, symmetric, antisymmetric, transitive, and equivalence relations.
9.Empty Relation
Meaning of an empty relation, how it is formed, and simple examples showing no pairs included.
10.Universal Relation
Meaning of a universal relation, how it includes all ordered pairs, and simple examples showing complete connection.
11.Reflexive Relations
Meaning of a reflexive relation, the self-pair condition, and simple examples to understand how every element relates to itself.
12.Irreflexive Relations
Meaning of an irreflexive relation, condition for no self-pairs, and simple examples.
13.Symmetric Relations
Meaning of symmetric relations, the two-way condition, and simple examples that show how pairs reverse.
14.Antisymmetric Relations
Meaning of antisymmetric relations, the condition for reversed pairs, and simple examples showing when elements can and cannot reverse.
15.Asymmetric Relations
Meaning of asymmetric relations, how they forbid reverse pairs entirely, and simple examples to understand strict one-way connections.
16.Transitive Relations
Meaning of transitive relations, the chain condition, and examples showing how links extend through a middle element.
17.Equivalence Relations
Meaning of equivalence relations, the three required conditions, and simple examples showing how they group elements.
18.Equivalence Class
Meaning of an equivalence class, how elements group together under an equivalence relation, and simple examples.
19.Partition of a Set (via Equivalence Relation)
Meaning of partition of a set, how equivalence relations break a set into disjoint groups, and simple examples.
20.Composition of Relations
Meaning of composition of relations, how two relations link through a middle element, with simple step-by-step examples.
21.Inverse of a Relation
Meaning of the inverse of a relation, how ordered pairs reverse, and examples showing how the direction of a relation flips.
22.Matrix Representation of Relations
Understanding how to represent a relation using a 0–1 matrix, with examples and interpretation.
23.Digraph Representation of Relations
Understanding how to represent a relation using a directed graph, with nodes and arrows showing connections.
24.Properties of Relations (Summary Table)
Quick summary of important relation properties like reflexive, symmetric, antisymmetric, asymmetric, and transitive.
25.Number of Possible Relations
How to count the total number of possible relations using the size of the Cartesian product, with simple formulas and examples.
26.Applications of Relations
Key applications of relations in classification, ordering, networks, functions, and real-world modelling.
27.Word Problems Based on Relations
Simple word problems involving relations with clear step-by-step interpretation into ordered pairs.