NCERT Solutions for Class 11 Maths Chapter 1 Sets

 

NCERT Solutions for Class 11 Maths Chapter 1 Sets: Set is a well-defined collection of objects. In our daily life, we use sets in many situations. In arranging books in a shelf we categorize it into different sets, such as a set of novels, a set of short stories, a set of science fictions, etc. In NCERT Solutions for Class 11 Maths Chapter, 1 Set introduces the concept of sets and operations on set. Let's consider an example of a survey in which 5 data are taken. 1. Gender 2. Age 3. weight. 4. waist diameter 5. Diabatic patient or not. Based on the obtained data two main sets are formed the namely diabetic patient and non-diabatic patient. Using these data we will be able to predict whether a new person in the given region will have diabetes or not. So the NCERT Solutions for Class 11 Maths Chapter 1 Sets is the basics of data analysis. The new technology of machine learning uses data for predictions and classifications. (More the data available more accurate will be the prediction). The NCERT Solutions for Class 11 Maths Chapter 1 is the basic unit for the Further Mathematics course.

The main topics of the NCERT for Class 11 Maths Chapter 1 Sets are listed below:

1.1 Introduction

1.2 Sets and their Representations

1.3 The Empty Set

1.4 Finite and Infinite Sets

1.5 Equal Sets

1.6 Subsets

1.7 Power Set

1.8 Universal Set

1.9 Venn Diagrams

1.10 Operations on Sets

1.11 Complement of a Set

1.12 Practical Problem

A brief summary of NCERT Solutions for Class 11 Maths Chapter 1 Sets are given below:

  • A set is a well-defined collection of objects
  • An empty set is a set which does not contain any element. It is represented by \phi or {}. The empty set is a subset of all the sets.
  • The power set of A is the collection of all the subsets of A. 
  • If a set A contains N elements then the power set of A contains 2n elements

Another important concept of NCERT Solutions for Class 11 Maths Chapter 1 is operations on sets. The Venn diagrams for basic operations are shown below

1. U represents universal sets, A and B represents sets A and B respectively

2. Union of A and B is represented by the green colour. Denoted by : \mathrm{A\cup B}

3. The intersection of set a and B is represented by green colour. Denoted by \mathrm{A\cap B}

4. A-B: A but not B. A-B is represented by red colour

We can solve many problems using operations on Sets. An example from NCERT Solutions for Class 11 Maths Chapter 1 Sets is given below.

Q)  In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?

Solution: Total number of students in class 35.

Number of students like to play cricket:  n(c)=24

Number of students like to play football: n(f)= 16

35=n(c)+n(f)-Number of students like to play both cricket and football

therefor Number of students like to play both cricket and football=40-35=5

This can be represented by a Venn diagram as follows

The complete Solutions of NCERT Class 11 Mathematics Chapter 1 is provided below:

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Exercise 1.1

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Exercise 1.2

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Exercise 1.3

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Exercise 1.4

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Exercise 1.5

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Exercise 1.6

NCERT Solutions for Class 11 Maths Chapter 1 Sets - Miscellaneous

NCERT Solutions for Class 11 Mathematics

Chapter-2

Relations and Functions

Chapter-3

Trigonometric Functions

Chapter-4

Principle of Mathematical Induction

Chapter-5

Complex Numbers and Quadratic equations

Chapter-6

Linear Inequalities

Chapter-7

Permutation and Combinations

Chapter-8

Binomial Theorem

Chapter-9

Sequences and Series

Chapter-10

Straight Lines

Chapter-11

Conic Section

Chapter-12

Introduction to Three Dimensional Geometry

Chapter-13

Limits and Derivatives

Chapter-14

Mathematical Reasoning

Chapter-15

Statistics

Chapter-16

Probability

NCERT Solutions for Class 11- Subject wise

NCERT Solutions for Class 11 Biology

NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Chemistry

NCERT Solutions for Class 11 Physics

 

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