Disjoint Sets are the Sets whose intersection with each other results in a Null Set. In Set Theory if two or more sets have no common elements between them then the Intersection of Sets is an Empty Set or Null Set. This kind of Sets is Called Disjoint Sets. Go through the entire article to know about Disjoint Sets Definition, Disjoint Sets using Venn Diagram, Pairwise Disjoint Sets, etc.
Disjoint Sets Definition
Two Sets are said to be disjoint if they have no common elements between them. If elements in two sets are common then they are said to be Non-Disjoint Sets. Condition for Disjointness is just that intersection of the entire collection needs to empty.
For Example, A = { 4, 5, 6} B = { 7, 8, 9} then A and B are said to be Disjoint Sets since they have no common elements between them. Some Sets can have null set as Intersection without being Disjoint.
Disjoint Sets using Venn Diagram
Two sets A and B are disjoint sets if the intersection of two sets A and B is either a null set or an empty set. In other words, we can say the Intersection of Sets is Empty.
i.e. A ∩ B = ϕ
Pairwise Disjoint Sets
Definition of Disjoint Sets can be proceeded to any group of sets. Collection of Sets is said to be pairwise disjoint if it has any two sets disjoint in the collection. These are also called as Mutually Disjoint Sets.
Consider P is a set of any collection of Sets and A and B. i.e. A, B ∈ P. Then, P is known as pairwise disjoint if and only if A ≠ B. Therefore, A ∩ B = ϕ.
Example:
{ {7}, {3, 4}, {5, 6, 8} }
Solved Examples on Disjoint Sets Venn Diagrams
1. Determine whether the following Venn Diagram represents Disjoint Sets or not?
Solution:
S = {2, 4, 6 8} T = {1, 3, 5, 7}
Sets S, T doesn’t have any common elements between them. Thus, Sets S, T are said to be Disjoint.
2. If A = { 1, 2, 3, 4, 5, 6, 7, 8, 9} B = {14, 15, 16, 17, 18, 19}. Check whether the following are Disjoint Sets are not?
Solution:
Given Sets are A = { 1, 2, 3, 4, 5, 6, 7, 8, 9} B = {14, 15, 16, 17, 18, 19}
Sets A, B doesn’t have any common elements between them. Thus, Sets A, B are said to be Disjoint.
