ICSE Class 11 Maths | 1. Sets and Functions by Pavan | Learn Smarter
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1. Sets and Functions

This chapter introduces sets and functions as foundational concepts in mathematics, exploring their definitions, types, and operations. It covers various methods for representing sets, including roster and set-builder forms, and delves into the properties of set operations. Additionally, the chapter defines functions, discusses their classification, and explains concepts like domain, co-domain, range, composition, and inverse functions.

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Sections

  • 1

    Sets And Functions

    This section introduces sets and functions, fundamental concepts in mathematics that organize and relate objects.

    Learning Practice

  • 1.1

    Introduction

    This section discusses the foundational importance of sets and functions in mathematics.

    Learning Practice

  • 1.2

    Sets

    Sets are defined as well-defined collections of distinct objects, with various types and operations.

    Learning Practice

  • 1.2.1

    Definition Of A Set

    A set is defined as a well-defined collection of distinct objects known as elements.

    Learning Practice

  • 1.2.2

    Types Of Sets

    This section discusses the various types of sets, including finite, infinite, empty, singleton, equal sets, subsets, proper subsets, and the universal set.

    Learning Practice

  • 1.2.3

    Representation Of Sets

    This section discusses the methods of representing sets, particularly roster and set-builder notation.

    Learning Practice

  • 1.2.4

    Operations On Sets

    This section covers the basic operations that can be performed on sets, including union, intersection, difference, and complement.

    Learning Practice

  • 1.2.5

    Properties Of Set Operations

    This section outlines the key properties governing operations on sets, including commutative, associative, distributive laws, and De Morgan’s laws.

    Learning Practice

  • 1.3

    Functions

    The section on Functions defines the concept and types of functions, including their domain, co-domain, range, composition, and inverse.

    Learning Practice

  • 1.3.1

    Definition Of A Function

    This section defines a function as a rule that assigns exactly one output from the co-domain for each input from the domain.

    Learning Practice

  • 1.3.2

    Domain, Co-Domain, And Range

    This section covers the definitions and relationships of domain, co-domain, and range in the context of functions.

    Learning Practice

  • 1.3.3

    Types Of Functions

    This section discusses various types of functions, including injective, surjective, bijective, and constant functions, highlighting their distinct characteristics.

    Learning Practice

  • 1.3.4

    Composition Of Functions

    This section explores the concept of composing functions to create a new function from two given functions.

    Learning Practice

  • 1.3.5

    Inverse Functions

    Inverse functions are functions that reverse the mapping of bijective functions.

    Learning Practice

References

m11-1.pdf

Class Notes

Memorization

What we have learnt

  • A set is a well-defined col...
  • Functions assign exactly on...
  • Sets can be classified into...

Final Test

Revision Tests