Class 11 Maths Chapter 2 Relations and Functions NCERT Solutions | Full Guide with Examples

Class 11 Maths Chapter 2 – Relations and Functions

Introduction

Relations and Functions form the foundation of higher mathematics. If you understand this chapter well, topics like calculus, algebra, and graphs become much easier.

A relation shows how elements of one set are connected to elements of another set. A function is a special type of relation where each input has only one output.

Basic Definitions

Relation:

A relation from set A to set B is a subset of A × B

Cartesian Product:
If A and B are two sets, then
A × B = {(a, b) | a ∈ A, b ∈ B}

Cartesian Product Formula

$$n(A \times B) = n(A) \times n(B)$$

Function:
A function is a relation where each element of A has exactly one image in B

Important Terms

• Domain: Set of all inputs

• Range: Set of actual outputs

• Codomain: Possible outputs

Types of Relations

• Empty Relation

• Universal Relation

• Identity Relation

• Inverse Relation

Types of Functions

• One-One Function

• Many-One Function

• Onto Function

• Into Function

Representation of Functions

• Roster Form

• Set Builder Form

• Arrow Diagram

• Graph

15 FAQs 

1. What is relation?

A relation is a subset of Cartesian product A × B.

2. What is function?

A function is a relation where each input has one output.

3. What is domain?

Set of all input values.

4. What is range?

Set of actual output values.

5. What is codomain?

Set of possible output values.

6. What is Cartesian product?

Set of ordered pairs from A and B.

7. Formula of A × B?

n(A × B) = n(A) × n(B).

8. What is identity relation?

Relation where every element is related to itself.

9. What is inverse relation?

Relation obtained by reversing ordered pairs.

10. Number of relations formula?

2^(n(A)×n(B)).

11. Number of functions formula?

(n(B))^(n(A)).

12. What is one-one function?

Each element has unique output.

13. What is many-one function?

Multiple inputs can have same output.

14. What is onto function?

Range equals codomain.

15. What is into function?

Range is subset of codomain.

$$\text{Number of relations from A to B} = 2^{n(A) \times n(B)}$$

Solved NCERT Examples (Step by Step)

Example 1

If A = {1,2} and B = {3,4}, find A × B

Solution:
A × B = {(1,3), (1,4), (2,3), (2,4)}

Example 2

Find number of elements in A × B

Solution:
n(A)=2, n(B)=2

n(A × B) = 2 × 2 = 4

Example 3

If A = {1,2}, B = {3,4}, find number of relations

Solution:
n(A × B) = 4

Number of relations = 2⁴ = 16

Example 4

Check if relation R = {(1,2),(2,3)} is a function

Solution:
Each element of domain has one image
So, it is a function

Example 5

Check if {(1,2),(1,3)} is a function

Solution:
Element 1 has two images
So, not a function

Example 6

Find domain and range of f = {(1,2),(2,3),(3,4)}

Solution:
Domain = {1,2,3}
Range = {2,3,4}

Example 7

If A = {1,2}, B = {a,b,c}, find number of functions

Solution:
n(A)=2, n(B)=3

Number of functions = 3² = 9

Example 8

Find inverse of relation R = {(1,2),(3,4)}

Solution:
R⁻¹ = {(2,1),(4,3)}

Example 9

Check if relation is identity

Solution:
If R = {(1,1),(2,2)}
Then it is identity relation

Example 10

Find range of function f(x)=x² for A={-2,-1,0,1,2}

Solution:
f(x) = x²

Range = {0,1,4}

Practice from Exercises

You should practice:

• Cartesian product questions

• Identifying relations and functions

• Domain and range problems

• Number of relations and functions

• Graph-based questions