Cbse Class 11 Maths Sets Complete Formula Guide

Sets are one of the integral parts of Class 11 mathematics. It introduces the set theory which is one of the basics for higher studies. Hence, the chapter is important and mustn't be neglected. The chapter is also slightly formula based and hence sets of formulas Class 11 are necessary.  For this reason, here we are presenting to you all the important sets of Class 11 Formulas. We will be discussing all the important formulas and with that, we'll also see the significance of each of the formulas.

Our expert faculty prepares the NCERT Solutions For Class 11 Maths Chapter 1 Sets following the latest CBSE Syllabus for 2021-22 as applied to 2019. The NCERT Solutions in Maths provide students with an effective and efficient process of solving problems. more effectively and efficiently. Furthermore, we focus on creating step-by-step solutions for all NCERT problems in a format that is easy to understand for students.

In Chapter 1 of the NCERT textbook, sets are used to define concepts of functions and relations. Class 11 Maths Chapter 1 from NCERT is devoted to a concept known as I. It contains basic definitions and operations related to sets. Since sequences, geometry, and probability are all built on Sets, it is essential to have a solid foundational knowledge of them. However, it is among the most straightforward chapters in NCERT Class 11 Maths to score maximum marks. These Vedantu NCERT Solutions are helpful for students who are looking for a simple and quick way of resolving questions.

What is a Set?

A set is a defined collection of objects. A set that contains a definite number of objects is called a definite set. Whereas a set consisting of an indefinite number of elements is called indefinite sets.

Example of a finite set: {1,2,3,4}.

Example of an infinite set: the set of all the natural numbers.

Now to understand all the formulas, firstly let us understand all the symbols used and what they signify.

1. When you want to unify or add two sets A and B, it is represented through A U B. Finding the union of two sets gives us a set containing all the elements contained in both A and B.

2. When you want to find the common elements between two sets A and B then, you need to find the set A intersection B or A inverted U B.

3. Sets can be added and subtracted.

4. You can also find A bar, this shall give you all the elements which are not contained in the set. This is called the complement of the set.

What is the Cardinality of a Set?

The cardinality of a set can be defined as the number of elements contained in a set. It could range from 0 to infinity.

For instance

Consider the set A = {1,2,3,4}.

The cardinality of set A is represented as n(A), which is 4 since A contains 4 elements.

Let's take another example for a better understanding:

Now consider the set of all the integers Z.

What would the cardinality of Z be?

Well, we do not know the number of integers hence the cardinality of the set Z would be indefinite.

Consider two sets of unknown cardinality:

A and B.

n(AᴜB) represents the total number of elements present in both of the sets A and B combined.

n(AᴜB) = n(A) + (n(B) – n(A∩B).

The Above-mentioned Formula is one of the most important formulae of set theory. It is used to find AᴜB. Let's understand this Formula in detail using a Venn diagram.

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The diagram given above is called the Venn diagram. It represents two different sets A and B. The region of the Venn diagram which is highlighted in pink are the elements that are common to both sets A and B. If we simply add the elements of A and B together,  the elements belonging to the pink part would be added twice and hence will give us an incorrect sum. Hence while finding the union of two sets we need to subtract the intersection of the two sets one time. This will negate the error caused earlier and find the perfect union between the two sets.

Now, let us jump to the next level and try understanding the formula for 3 different sets:

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Consider 3 sets intersecting like in the Venn diagram given above.

n(AUBUC) = n(A) + n(B) + n(C) – n(A⋂B) – n(B⋂C) – n(C⋂A) + n(A⋂B⋂C)

From the image, we can visualize that if we simply add the sets together, some of the regions will be added multiple times. Hence, using this Formula we rectify the error and subtract the regions that have been added multiple times.

What Differentiates NCERT Solutions for Class 11 Maths Chapter 1- Sets from Others

This chapter consists of six exercises and a miscellaneous exercise designed to help students understand the concepts related to Sets of Class 11 Maths CBSE Syllabus (2021-22) thoroughly. NCERT Solutions for Class 11 Maths explains the following topics in Chapter 1:

1. A set is a collection of objects with a well-defined structure.

2. When there is no element in a set, then it is called an empty set.

3. Sets with definite numbers of elements are defined as finite sets
   Sets consisting of infinite elements are defined as infinite sets

4. If two sets A and B contain the same elements, then they are considered equal.

5. When every element of a given set A is also an element of another set B, a set A is said to be a subset of another set B. R can be broken down into intervals.

6. There are multiple subsets of a set A which comprise a power set. They are indicated by P(A).

7. Those elements that are either in A or B are found in the set A+B, which is the union of two sets A and B.

8. A set of all elements which are common to two different sets A and B is the intersection of the two. Those elements that belong to A, but not to B, make up the difference between two sets A and B in this order.

9. Among all the elements of a universal set U, the complement of a subset A is a set of all elements that are not also elements of A.

10. A and B are equivalent. That is, (A + B)' = A′ * B′ and (A + B)' = A'*B'.

Solved Examples Sets Class 11 Maths

Example 1: In a school, there are 200 children, 65 like drawing and 85 like music. 25 like both. Find out how many of them like either of them or neither of them?

Solution:

Total number of children, n(μ) = 200

Number of children who enjoy drawing, n(d) = 65

Number of children who enjoy music, n(m) = 85

Number of students who like both, n(d∩m) = 25

Number of students who like either of them,

n(dᴜm) = n(d) + n(m) – n(d∩m)

→ 65 + 85 - 25 = 125

Number of students who like neither = n(μ) – n(dᴜm) = 200 – 150 = 50.