A set can be well-defined collection of objects, where the elements are fixed and cannot vary there are various other ways that we will be able to have the definition for as well. This is also important because that way we will be able to understand what will be the patterns the numbers are being represented.
In Class 11 maths, we will try and learn about different types of sets that are being able to identify the different types as well.
Types of Sets
We will try and understand the different types of set
Empty Sets
The set where we will not find any elements or null elements which is also called a Null set or Void set. It is often denoted by {}.
For example: Let, Set X = {x:x is the number of students studying in Class 6th and Class 7th}
Singleton Set
This means that the set have only one element. There is no other element present in the set.
For example, Set X = { 2 } is a singleton set.
Finite and Infinite Sets
Finite sets will always have finite number of elements, and on the other hand the infinite sets will always have the number of elements cannot be estimated, but it has some figure or number.
For example, Set X = {1, 6, 3, 4, 5} is a finite set, as it has a finite number of elements in it.
Equal Sets
We can say that the two sets X and Y are equal if every element of set X is also the elements of set Y and if every element of set Y is also the elements of set So we will see that that same elements are present in each set.
X = Y
For example, Let X = { 1, 6, 3, 4} and Y = {4, 3, 6, 1}, then X = Y
So the two sets will be equal if the same elements are present in each of the set.
Subsets
A one of the set is said to be the subset of the other is we can see that the elements of one set is also present in the bigger set as well It is denoted with the symbol as X ⊂ Y.
X ⊂ Y if a ∊ X ⇒ a ∊ Y
So, this is a universally accepted process that every set is a subset of its own
Power Sets
The power set is said to be the super set of all subsets. So if we have to explain it further,
We know the empty set is a subset of all sets and every set is a subset of itself. So taking forward into this we will have of set X = {2, 3}. From the above given statements we can write,
{} is a subset of {2, 3}
{2} is a subset of {2, 3}
{3} is a subset of {2, 3}
{2, 3} is also a subset of {2, 3}
Therefore, power set of X = {2, 3},
P(X) = {{}, {2}, {3}, {2, 3}}
Universal Sets
A universal set is defined as a set that which contains all the elements of other sets. The universal set is represented as ‘U’.
For example; set X = {1, 2, 3}, set Y = {3, 4, 5, 6} and Z = {5, 6, 7, 8, 9}
Then, we can also write the universal set as, U = {1, 2, 3, 4, 5, 6, 7, 8, 9,}
Union of sets
A union of two sets is defined as the union of all the sets. It is denoted by ⋃.
For example, set X = {2, 5, 7} and set Y = {4, 9, 8}
Then union of set X and set Y will be;
X ⋃ Y = {2, 5, 7, 4, 9, 8}
Intersection of Sets
We will see that it is the set of all elements that are common to all the given sets, and then it will give intersection of sets. It is denoted by the symbol ⋂.
For example, set X = {2, 3, 7} and set Y = {2, 4, 9}
So, X ⋂ Y = {2}
The sets are the important representation because that way they will be able to have differentiated the numbers.
