All Formulas of Sets Class 11
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.
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.
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.
Sets can be added and subtracted.
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:
A set is a collection of objects with a well-defined structure.
When there is no element in a set, then it is called an empty set.
Sets with definite numbers of elements are defined as finite sets
Sets consisting of infinite elements are defined as infinite setsIf two sets A and B contain the same elements, then they are considered equal.
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.
There are multiple subsets of a set A which comprise a power set. They are indicated by P(A).
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.
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.
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.
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.
FAQs on CBSE Class 11 Maths Sets Formulas
1. Can I get a List of all Sets of Chapter Class 11 Formulas?
Given below is the formula list of all the formulae of the chapter sets class 11.
n(AᴜB) = n(A) + (n(B) – n(A∩B).
n(AUBUC) = n(A) + n(B) + n(C) – n(A⋂B) – n(B⋂C) - n(C⋂A) + n(A⋂B⋂C).
If n(A∩B)= 0 then AᴜB = n(A) + n(B).
n(A - B) + n(A∩B) = n(A).
N(B - A) + n(A∩B) = n(B).
n(AᴜB) = n(A - B) + n(A⋂B) + n(B - A).
The formulas given above are all you need for solving almost all the types of problems that you would encounter related to set theory. Knowing these formulas would enable you to solve even the toughest questions.
2. Why do you Need the Set Formula List Class 11?
The formula list given above consists of all the formulae needed to solve any kind of problem from the chapter set theory. Remembering these formulas is very vital since the chapter is highly formula based. Although you needn't mug up all the formulae, you must understand each formula from their Venn diagram. You must also understand how the formula was derived from the Venn diagram. However, additionally remembering the formulae would make it easier for you to solve the problems at a quicker pace since you cannot put in effort into deriving the formula every single time!
3. An analysis of 600 students across a school found 150 taking tea and 225 taking coffee, while 100 also took both tea and coffee. Identify the number of students who did not drink tea or coffee?
Based on our assumptions, we can say, the set U consists of all the respondents to the survey while the set T consists of students who are taking tea
C = the set of the students taking coffee
Total number of students in a school, n (U) = 600
Number of students taking tea, n (T) = 150
Number of students taking coffee, n (C) = 225
AlTo determine the number of students who are not drinking tea or coffee, we need to find (T * C).r tea i.e. n (T ∩ C’)
∴ According to the question,
n ( T ∩ C’ )= n( T ∩ C )’
= n (U) – n (T ∩ C)
= n (U) – [n (T) + n(C) – n (T ∩ C)]
= 600 – [150 + 225 – 100]
= 600 – 275
= 325
∴ Number of students taking neither coffee nor tea = 325 students
4. What topics are covered by NCERT solutions for Class 11 Maths?
Topics covered in Chapter 1 of NCERT Solutions for Class 11 Mathematics are:
1. Introductory remarks
2. An introduction to sets and their representations- Sets, their formulas, and the nature of their representation in general
3. There is only one set, the empty one, which is a set with no elements; its cardinality or size is zero. Axiomatic set theories that include an axiom of the empty set should ensure that the empty set exists. Other set theories can deduce its existence from other premises.
4. Sets, definite and indefinite
5. Sets of equal value
6. Sets of subsets
7. Set of power
8. Set of universal tools
9. A Venn Diagram
10. Operational procedures on sets
11. Completion of a set
12. Examples of unions and intersections of two sets
5. Do you have any tips for preparing for Class 11 Maths?
Students in Class 11 can benefit from some helpful tips for preparing for the Maths exam and acing it.
Consider your options: Make a checklist dividing the subjects into their chapters and starting by listing out the subjects. Identify the areas where you know you are strong, then practice as many exam-style questions as you can. You should then start looking at the chapters where you have weaknesses once you are done with these concepts. concepts. Begin by making notes on these subjects, then practice questions from previous year papers. Update the chapters in the checklist on a daily or weekly basis to ensure you are aware of your progress.
Write down your notes: The first step is to study regularly and complete your CBSE Class 11 Maths Syllabus on time. You should complete your projects, assignments, and practicals on the day they are assigned so you can move on to your next task. If you find some chapters difficult, then you can slowly advance to them. Even the most difficult topics, once the basics are brushed up, will become easier to understand.
Identify and solve sample papers: Students can improve their test-taking skills by solving sample papers. Students should also try to solve previous year's question papers. The question patterns and marking schemes will become clearer when they examine previous year's papers.
Check out the Question Paper: It is recommended that students review the Maths question paper before starting to solve it. They should identify which questions they can master easily. Save time by solving the problems you are certain of so that other questions can be answered more quickly. Be sure you have attempted the questions which have a good weighting and those questions are not missed.
