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Types of Sets | Equivalent Sets | Singleton Set | Empty Set or Null Set

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Types of sets
There are many types of set. I will try to explain some types in the following.
Finite set
The set having the limited number of elements is called finite set. For example
A=The set of first five natural numbers.
B=The set of whole numbers less than fifteen.
C={1,2,3,4,5,6,7,8,9,10}
In the above-mentioned examples, the given sets have limited number of elements so that they can be said the finite sets. Always remember that the last number of finite set can be founded.
Infinite set
If a set has unlimited number of elements is called infinite set. For example
A= {1,2,3,4,5,6,7, ...................}
B= The set of prime numbers
n the above-mentioned examples, the given sets have unlimited number of elements so that they can be said the infinite sets. Always remember that the last number of infinite set cannot be founded.
Singleton set
If a set has only one element then it is called singleton set. For example, A = {1}
Null/Void/Empty set
If a set has no element then it is called empty set. For example
A=The set of two hundred feet tall boys.
B= The set of flying dogs.
In the above given examples there are no hundred feet tall boys and flying dogs so that these are empty sets. It is written as { }.
Equal sets
If two sets have same elements they are called equal sets. For example
A= {1,2,3,4}
B= {4,3,2,1}
Both sets A & B have same elements they are called equal sets.
Equivalent sets
If two sets have same number of elements then they are called Equivalent sets. For example
A={a,s,d,f,g,h,j}
B= {1,2,3,4,5,6}
Both sets A&B have 6 , 6 elements they are called equivalent sets.
Non-equivalent sets
If two sets have different number of elements then they are called non-equivalent sets. For example
A={a,s,d,f,g,h,j,k}
B= {1,2,3,4,5}
Both sets A&B have different number of elements so that they are called non-equivalent sets.
Subset
If all elements of set A are present in set B then set A is called subset of B. For example
A = {1,2,3,4}
B = {1,2,3,4,5}
In the above-mentioned example all the elements of set A are present in set B so A is called the subset of set B.
Proper subset
If all elements of set A are present in set B and all the elements of set B are not present in set A then A is called proper subset of B. For example
A = {1,2,3,4}
B = {1,2,3,4,5}
In the above-mentioned example all the elements of set A are present in set B and all the elements of set B are not present in set A. so A is called the proper subset of set B.
Improper subset
If all elements of set A are present in set B and all the elements of set B are present in set A then A is called improper subset of B. For example
A = {1,2,3,4}
B = {1,2,3,4}
In the above-mentioned example all the elements of set A are present in set B and all the elements of set B are also present in set A. so A is called the improper subset of set B.
Super set
If set A is subset of set B then B is called superset of set A. For example
A = {1,2,3,4}
B = {1,2,3,4,5}
In the above-mentioned example set A is subset of set B then B is called superset of set A.
Overlapping sets
If two sets are not subset of each other and at least one element is common in between them so they are called overlapping sets.
For example
A={4,5,6,7,8}
B={1,2,3,8,9}
In above example set A and B has one common element they are called overlapping sets.
Disjoint sets
If two sets have no common elements is they are called disjoint sets.
For example
A={4,5,6,7}
B={1,2,3,8,9}
In above example set A and B has no common element they are called disjoint sets.
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