Hey, in this post you will get set class 11 notes in simple language with lot of examples. Here is the list of topics that are going to cover in this article.

Definition of set

Way of representing a set :[Roster form and set builder form].

Types of the set with definition and example

Subsets

Universal set

Power set

Operation of set:[Union, intersection, disjoint, and complement of the set].
So, let’s dive into the given topic step by step and discuss every topic for set class 11 notes completely .
DEFINITION AND TYPES OF SET
SET: Set is the collection of welldefined objects.
For example, the collection of allnatural numbers is set because it is welldefined but, the collection of all good smartphones is not set because it is not welldefined, many smartphones can be in good in different features.
Note:
1. All sets are collection but all collections need not be set, for the set, a collection must be welldefined.
2. Objects in a set are called elements.
These points are really important and basic of set class 11 notes.You should
There are two ways of representing a set
1.Roster form(tabular form)
2.Setbuilder form
ROSTER FORM: When the elements of a set are separated by commas, within braces{ } is called in Roster form.
Example: The set of vowels of the English alphabet may be represented as { a,e, I,o,u }.
SETBUILDER FORM: When the elements of the set are described by the statement within the Braces { } is called in setbuilder form.
Example: The set of all prime numbers less than 10 can be represented as
P= {x:x is prime numbers less than 10}
where“:” sign read as `such that ‘.
Set class 11 notes:[TYPES OF SETS]
There are six types of set
 Empty set
 Singleton set
 Finite set
 Infinite set
 Equivalent set
 Equal set
EMPTY SET: A set is said to be empty or null or void set if it has no element and it is denoted by Φ.In roaster form, it is denoted by { }.
example: In roaster form
(i) {x∈R:x²=4 }=Φ.
(ii) {x∈R:2<x<3 }=Φ.
In setbuilder form
(i) The set is given by A={x:x ∈R and x²=9 }
Singleton set: A set consisting of a single element is called a singleton set.
example: In roster form
(i) The set {5} is a singleton set because it has only one element.
In setbuilder form
(i)The set {x:x ∈N and x²=9} is singleton set because we can put two values of x to satisfy this equation i.e 3,3 but x should belong to a natural number.so, we have only 3 as a solution.
Finite set: A set is called finite set if it is either empty set or its element can be counted in natural numbers 1,2,3,4,……etc.
Cardinal number of a finite set: The number of elements present in finite set is called a cardinal number of the set. It is denoted by n(A).
suppose a set A={4,6,6,3,0,1,}. it is a finite set because we can count the no of elements. The number of elements in set is 6 so its cardinal number will be n(A) =6.
Infinite set: A set whose elements cannot be listed by natural number (no of the element in the set is infinite ) is called an infinite set.
Example – (i) set of all points in the plane.
(ii) set of lines can pass through a point.
(iii) set of real numbers between two natural numbers.
 Cardinal number of infinite sets is infinite i.e n(A)=∞
Equivalent sets: Two finite sets A and B are equivalent if their cardinal numbers are the same i.e no of the element in both sets should be the same.
example: Set A ={1,2,3,4,5,6}
Set B={a,b,c,d,e,f}
here, both sets have the same no of element but they are different.
Equal set: Two sets A and B are said to be equal if every element of set A belong to set B, and every element of set B belong to set A i.e The cardinal number of both sets should be equal with the same elements
example If A={1,2,4,5,6} and B={5,6,4,2,1}. Then A =B because the cardinal number of both sets is equal with the same element.
Conclusion: Every equal set is the equivalent set but every equivalent set need not be equal.
Set class 11 notes:{Subset}
Let A and B be two sets. If every element of set A belongs to set B, then A is called a subset of B and it is denoted A⊆B, which is read as ” A is a subset of B ”.
Example Let A ={1,2,3,4,5} and B={1,2,3,4,5,6} .
Here Every element of set Abelong to set B
∴ A⊆B
Note :(i)A is a subset of B, we say that B contains A or B is a superset of A and we write B⊃A.
(ii) If A is not a subset of B, we write A⊄B.
Subsets are further categorized as a proper and improper subset
Proper subset: A subset is called proper subset if A is a subset of B but A≠B.Above example is a proper subset
Improper subset: A subset is called an improper subset if every element of A belong to B i.e A=B
Example: All equal sets are an example of improper subsets.
 Every set is a subset of itself.
 The empty set is a subset of every set.
 An empty set is a proper subset of any set because only one element belongs to another set not all.
 Total number of a subset of the finite set containing n elements is 2^n
Universal set
The universal set is a set that contains all the set . it is a super set of all the set and it is denoted by U.
Example : If A ={1,2,3} , B={2,4,5,6} and c={1,3,5,7} ,then universal set is given by U={1,2,3,4,5,6,7}
Power set
Let A be a set. then the collection or family of all subsets of A is called the power set of A and denoted by p(A).
since the empty set and the set, A itself are subsets of A
Example Let A={1,2,3}.then ,the subsets of A are :Φ,{1},{2},{3},{1,2},{1,3},{2,3}and {1,2,3}.Hence ,p(A)={Φ,{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}but If A is an Empty set ,then p(A) has just one elementΦ i.ep(A)={Φ}.
Set class 11 notes:[Operations on sets]
Union of sets
Let A and B be two sets .the union of A and B is the set of all those elements which belong either ti A or to B or to both A and B .we shall use the notation A ⋃B(read as “A union B “) to denote the union of A and B .
thus, A⋃B={x:x∈A or x∈B}
Example Let A={1,2,4,5,6}and B={a,b,c,d}
∴ A⋃B={1,2,4,5,6,a,b,c,d}
Intersection of sets
Let a and B be two sets.The intersection of A and B is the set of all those elements that belong to both A and B.The intersection of A and B is denoted by A⋂B(read as “An intersection B”)
Example Let A={1,2,4,5,6}and B={2,4,3}
∴ A⋂B={1,2,3,4,5,6}
The intersection of above example of union
Example Let A={1,2,4,5,6}and B={a,b,c,d}
∴ A⋂B=Φ
Disjoint sets
Two sets A and B are said to be disjoint ,if A⋂B=Φ
Example Let A={1,2,4,5,6}and B={a,b,c,d}
A⋂B=Φ
If A⋂B≠Φ, hen A, and B are said to be intersecting or overlapping sets.
Difference of sets
Let A and B be two sets. the difference of A and B, written as AB, is the set of all those elements of A which do not belong to B.
Thus AB={x:x∈A and x∉B}
similarly, the difference of BA is the set of all those elements of B that do not belong to A
thus BA={x:x∉A and x∈B}
Example If A={2,3,4,5,6,7] and B={3,5,7,9,then AB={2,4,6}because these element are not present in B .similarly because these elements are not present in A.
Symmetric difference of two sets
Let A and B be two sets .the symmetric difference of sets A and B is the sets(AB)⋃(BA) and is denoted by AΔB.
we have AB={2,4,6} and BA={9,11,13} from above example so,
(AB)⋃(BA)={2,4,6,9,11,13}
Complement of a set
Let U be the universal set and let A be a set such that A⊂U.then the complement of A with respect to U is denoted by A’ or UA and is defined as the set of all elements of U which are not in A.
Example Let U={1,2,3,4,5,6} and A={1,2}
∴ UA={3,4,5,6}
Set class 11 notes:[Law of algebra]
Idempotent law
Statement: For any set A, A∪A=A and A∩A=A
Example: Let set A={1,2,3},
According to Idempotent law, A∪A=A and A∩A=A.Let’s check this
A∪A={1,2,3}∪{1,2,3}={1,2,3}=A {According to definition of union of set}
A∩A={1,2,3}∩{1,2,3}={1,2,3}=A {According to definition of intersection of set }
Identity law
Statement: For any set A, A∪Φ=A and A∩U =A
Example: Let set A={1,2,3},
According to identity law, A∪Φ=A and A∩U =A
As we all familiar with about Φ and U.These are the symbol to denote Empty set and universal set
A∪Φ={1,2,3}∪Φ={1,2,3}=A
A∩U={1,2,3}∩U={1,2,3}=A
Cumulative law
Statement: For any sets A and B ,A∪B=B∪A and A∩B=B∩A
That is why we can say that union and intersections of sets are always cumulative
Associative law
Statement: If A , B, and C are three sets, then (A∪B)∪C=A∪(B∪C) and A∩(B∩C)=(A∩B)∩C
i.e union and the intersection of sets are always associative
Distributive laws
Statement: If A,B and C are three sets ,then A∪(B∩C)=(A∪B)∩(A∪C) and A∩(B∪C)=(A∩B)∪(A∩C)
i.e Union and the intersection of set are distributive over intersection and union respectively
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