Sets And its Types

In mathematics, the collection of different objects resulting in the formation of a group can be defined as sets. This collection may be of any group which contains items such as a collection of vehicles, numbers, numbers of days a week, and so on. Whenever we write this collection, we use a curly bracket, {}. Some examples of sets are as follows:

{1, 3, 5, 7, 9} (the first five odd numbers), {4, 6, 8, 10} (four even numbers). There are various different kinds of notations which we use to represent the elements present in the sets. Some of them are the semantic form of notation, set builder form of notation, and roster form of notation. In this article, we will try to cover some basic aspects related to sets such as types of sets, representation of the elements of sets, and do a detailed analysis about it. 

Different Types of Sets

As mentioned above, the collection of different objects resulting in the formation of a group can be defined as sets. In this section, we may cover the various types of sets. Some of them are mentioned below:

1. A type of set that consists of only one type of element can be defined as the singleton set. For example, A = {3}. 
2. A type of set that consists of a finite number of sets or the number of sets that can be counted can be denied as finite sets. For example, {2, 3, 5, 7, 9}, this set includes 5 elements. 
3. The opposite of finite sets is regarded as infinite sets. The collection of elements that cannot be counted. For example, multiples of 4 = {4, 8, 12, 16, 20} and so on. 
4. A set that does not consist of any type of element is known as the null or empty set. For example, {}: No elements. If you want to learn about Sets and their types in a detailed manner, in a fun way, and in an interactive manner. Visit Cuemath Website. 
5. If the numbers of elements in two different sets are the same, then the set is defined as equivalent sets. For example, {2, 3, 5, 7, 9} and {1, 3, 4, 7, 9}: Both sets consist of 5 elements. 
6. Whenever one element is different in two sets, then the sets are regarded as unequal sets. For example, {2, 3, 5, 7} and {2, 3, 5, 8}.
7. When the elements are the same in two different sets, then the set is known as the equal set. For example, {2, 3, 4} and {2, 3, 4}. 
8. When the elements are not common in two different sets, the set is defined as the design set. For example, {2, 3, 5, 7, 9} and {1, 3, 4, 7, 9}. 
9. The collection of each and every element in the universe is said to be a universal set that is symbolized by the block letter ‘U’. 
10.  The subsets present in the sets are defined as the power sets. When two sets overlap each other, then the set is defined as the overlapping set. 

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