Class 12 Mathematics Notes
🔹 Chapter 1: Relations and Functions
1.1 Relation
Definition:
A relation describes the way elements of one set are associated or connected with elements
of another set.
Formally, if A and B are two sets, then a relation R from A to B is a subset of the Cartesian
product A × B.
So,
R⊆A×B
A is called the domain (the set from which elements are taken).
B is called the codomain (the set to which elements are related).
The actual set of values related is called the range.
✅ Example:
Let A = {1, 2, 3} and B = {a, b}.
Then,
A × B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.
Now, a relation R can be:
R = {(1,a), (2,b)}.
This means:
1 is related to a
2 is related to b
1.2 Types of Relations
1. Reflexive Relation
o A relation R on set A is reflexive if every element is related to itself.
o i.e., (a,a) ∈ R for all a ∈ A.
✅ Example:
For A = {1,2,3},
R = {(1,1), (2,2), (3,3)} is reflexive.
🔹 Chapter 1: Relations and Functions
1.1 Relation
Definition:
A relation describes the way elements of one set are associated or connected with elements
of another set.
Formally, if A and B are two sets, then a relation R from A to B is a subset of the Cartesian
product A × B.
So,
R⊆A×B
A is called the domain (the set from which elements are taken).
B is called the codomain (the set to which elements are related).
The actual set of values related is called the range.
✅ Example:
Let A = {1, 2, 3} and B = {a, b}.
Then,
A × B = {(1,a), (1,b), (2,a), (2,b), (3,a), (3,b)}.
Now, a relation R can be:
R = {(1,a), (2,b)}.
This means:
1 is related to a
2 is related to b
1.2 Types of Relations
1. Reflexive Relation
o A relation R on set A is reflexive if every element is related to itself.
o i.e., (a,a) ∈ R for all a ∈ A.
✅ Example:
For A = {1,2,3},
R = {(1,1), (2,2), (3,3)} is reflexive.
