Complement of Set

Define Set.

In mathematics, a set is  defined as a collection or grouping of well- defined objects.  For example, N is the set of all natural numbers, then N = {1, 2, 3, 4, 5,….,∞}.

What is the Complement of a Set?

The complement of a set is the set that contains all the elements of the universal set which are not included in the given set and mathematically can be expressed for a set S as:

S’ = {x ∈ U : x ∉ S}

Write De Morgan’s Laws for the Complement of a Set.

De Morgan’s laws states:

• Complement of the union of two sets is equal to the intersection of the complements of the two sets, i.e., (S U T)’ = S’ ∩ T’.
• Complement of the intersection of two sets is equal to the union of the complements of the two sets, i.e., (S ∩ T)’ = S’ U T’.

What is the Complement of the Empty Set?

The empty set contains no elements however the set which contains all the possible elements is the universal set. Hence the complement of the empty set is the universal set.

What is Venn Diagram?

Venn Diagram is the diagram to represent set and their interaction using circles. 

Complement of a Set is one of the important operations, we can perform on a set in set theory. Grouping numbers with similar properties together, i.e., arranging them in sets is what forms the foundation for the rest of mathematics, thus set theory holds a very important place in the study of mathematics.

Having learned the importance of set theory, it is important to go through all its aspects to fully grasp its concept. In this article, we will learn about a particular aspect of set theory: complement of a set: its meaning, symbol, properties, and Venn diagram.