---
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entity_type: "chapter"
id: "66dfdf0e3f8b4e9e69bf7dd4"
title: "Relations and Functions"
board: "CBSE"
curriculum: "CBSE"
class: "Class 12"
subject: "Mathematics"
book: "Mathematics Part - I"
chapter: "Relations and Functions"
chapter_slug: "relations-and-functions"
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last_updated: "2026-06-20"
---

# Relations and Functions
This chapter focuses on the mathematical concepts of relations and functions. It revisits the definitions of domain, co-domain, and range from Class XI, providing a foundational understanding through examples that illustrate how two objects or quantities may be related.

---

## Knowledge Snapshot

| Field | Details |
| :--- | :--- |
| Class | Class 12 |
| Subject | Mathematics |
| Book | Mathematics Part - I |
| Chapter | Relations and Functions |
| Pages | 1-17 |

---

## Chapter Summary

### Short Summary
This chapter covers the definitions and types of relations and functions, their compositions, and relevant mathematical operations.

### Detailed Summary
The chapter begins by recalling prior knowledge of relations and functions, including domain, co-domain, and range. It discusses how the concept of relation in mathematics is analogous to its meaning in English, where a relation connects two objects or quantities. An example is given with sets of students from Class XII and Class XI, illustrating various types of relations. A formal mathematical definition of a relation as a subset of $A 	imes B$ is provided, along with notation for denoting relationships. The chapter concludes by stating that functions are a special kind of relation and outlines that different types of relations, functions, their compositions, invertible functions, and binary operations will be studied.

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## Topic-Wise Explanation

### Introduction
This section introduces the fundamental concepts related to relations and functions, emphasizing their relevance and applications in mathematics.

### Types of Relations
The chapter explains the various types of relations that can exist between sets, including examples to illustrate their nature.

### Types of Functions
This section describes different function types, detailing specific characteristics that distinguish them from general relations.

### Composition of Functions
The composition of functions is explored, illustrating how functions can be combined to create new mappings.

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## Core Ideas

| Idea | Explanation |
| :--- | :--- |
| Relations | A mathematical relation is a subset of a Cartesian product of two sets, establishing a connection between their elements. |
| Functions | Functions are specific types of relations where each input is mapped to exactly one output. |

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## Key Concepts

| Concept | Meaning |
| :--- | :--- |
| Domain | The set of all possible input values for a function. |
| Co-domain | The set of possible output values derived from the function. |
| Range | The actual set of output values that a function produces from its inputs. |

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## Important Points for Revision
* Definitions of relations and functions.
* Types of relations and examples.
* Characteristics of different types of functions.
* Concept of composing functions.
* Application of relations in real-life scenarios.
* Understanding domain, co-domain, and range.
* Notation for denoting relations.
* Properties of invertible functions.
* Introduction to binary operations.

---

## Vocabulary and Glossary

| Word / Phrase | Meaning |
| :--- | :--- |
| Relation | A connection between two sets represented as a subset of their Cartesian product. |
| Function | A relation where every element in the domain is associated with exactly one element in the co-domain. |

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## Practice Questions

### Short Answer Questions
1. Define a relation in the context of sets.
2. What is the difference between domain and range?
3. Provide an example of a function.
4. Describe what an invertible function is.
5. Explain the composition of two functions.

### Long Answer Questions
1. Define and explain the concept of relations between two sets with examples.
2. Discuss different types of functions and their unique properties.
3. Illustrate the process of function composition with mathematical examples.

---

## Related Concepts
* Domain
* Co-domain
* Range
* Invertible Functions
* Binary Operations

---

## Source Attribution

| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 66dfdf0e3f8b4e9e69bf7dd4 |
| Canonical URL | https://www.edzy.ai/cbse-class-12-mathematics-mathematics-part-i-relations-and-functions |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-12-mathematics-mathematics-part-i-relations-and-functions.md |