Union, intersection and complement of sets

A well-defined collection of different data and objects is known as a set. The objects of the data belong to the same group but each data is different from the other. While exploring more about sets, an individual needs to understand the concept of the union of a set, the intersection of a set and the complement of a set. 

Different Types Of Sets:

• Singular Set:

It is a set having only one element.

• Null set:

A set with no element present is known as a null set. It is mainly used to give a detailed explanation of different situations or parameters. 

• Finite set:

A set containing a finite number of elements is known as a finite set. Learners must note that the amount of the elements do not play an important role in this condition. 

• Infinite set:

An infinite set is known as that set that contains an infinite number of elements. There are high chances of getting an infinite set. Elements present in all sets of natural numbers will be infinite. 

What Are Set Operations?

Some chances sometimes sets do not have any particular data in common.  These types of sets are known as mutually independent sets. Let us have a look at different relations among the sets:

• Union Of A Set:

Union set is a set that consists of the various elements that are present in Sets A or B. An element in the Union of a set can be found in Set A or Set B. Mathematically, Union of a Set is defined as, if x ∈ A ∪ B, then x ∈ A or x ∈ B. 

Properties of the set are mentioned below:

• The commutative property states that A∪ B= B ∪ A
• A∪U=U
• A∪∅=A
• Associative property states that (A ∪ B) ∪ C= A ∪ (B ∪ C)

What is The Complement Of A Set?

The complement of a set refers to a set that has all the elements apart from the elements present in letting us suppose Set A. Therefore, the union of Set A and the complement of set A is Universal set, whereas the intersection of Set A and the complement of Set A is null.

Properties of this set are mentioned below:

• A∪A’=U
• A∩A’=∅

What Is The Intersection Of Sets?

The intersection of sets can be defined as a set containing all the elements present in Set A that is also present in Set B and vice versa. ‘AND’ is used to describe the condition of the intersection of sets. Thus, it can be said that elements that are present in the intersection of sets are present in bothSet A and Set B. 

The symbol “∩” is placed between the two sets A and B, written as A∩B to denote the intersection of Set A and Set B. The mathematical definition for the intersection of sets can be written in symbols as if x ∈ A ∩ B, then x ∈ A and x ∈ B.

Properties of this set are mentioned below:

• The commutative property states that A∩ B= B∩ A
• A∩U=A
• A∩∅=∅
• Associative property states that (A∩ B) ∩ C= A∩ (B ∩ C)

What is De Morgan’s Law?

De Morgan’s law deals with all three of the complement, union, and intersection of the sets. 

According to this law 

For the two sets A and B,

(A∪B)’= A’∩B’

Conclusion:

Mathematics is a branch that deals with the practical aspects of life. Various operations are involved in this branch such as associative, cumulative and distributive properties. The complement, union and intersection of sets are different aspects of mathematics that are connected. They are explained according to the De Morgan law and Venn diagram.