In this chapter we will learn to represent disjoint sets using Venn diagram.
Let’s first review the basics of disjoint sets.
What are disjoint sets?
Two sets are said to be disjoint if there are no common elements between the two.
The disjoint sets after intersection will return an empty set.
If A & B are two disjoint set, then; A ∩ B = 𝜙
Venn diagram representation of Disjoint set
To understand the below content you should have basic understanding of Venn diagram.
To learn the basics of Venn diagram in set theory, click the red link.
If Set A & B are disjoint set then the Venn diagram is represented as;
In the above image;
⟹ Rectangular box represent universal set
⟹ Circle A & B represent set A & B respectively.
Since there is no common element between set A & set B, there is no overlapping between the two circles.
Venn diagram Representation of Non Disjoint set
If two sets A & B are non disjoint, it means that there are common elements between the two sets.
Venn diagram representation of Non – Disjoint set is given below;
Since there are common elements between the two sets, both the circles intersect each other.
Examples of Disjoint set with Venn diagram
(01) Given below are two sets A & B. Represent the sets in Venn diagram.
A = { 2, 4, 6, 8 }
B = { 3, 5, 7, 9}
Solution
Since both the sets do not have common elements, they are disjoint set.
In the above image;
⟹ Rectangular box represents universal set.
⟹ Circle A & B represent set A & B.
Both the circles are not overlapping since there are no common elements between set A & B.
(02) Given below are two sets P & Q. Represent the sets in Venn diagram.
P = { Monday, Wednesday, Friday }
Q = { Tuesday, Thursday, Saturday, Sunday}
Solution
There are no common elements among both the sets. Hence, the set P & Q are disjoint set.
This means that intersection of both the sets results in empty set.
P ∩ Q = 𝜙
Representing the above sets in Venn diagram.
Example 03
Represent the below sets M & N in Venn diagram
M = { x : x is prime number less than 11 }
N = { y : 10 < y < 15 }
Solution
Let’s first represent the set in Roster form.
M = { x : x is prime number less than 11 }
M = { 2, 3, 5, 7 }
N = { y : 10 < y < 15 }
N = { 11, 12, 13, 14 }
Observe both the sets M & N. Note that there is no common element present in both sets.
Hence, sets M & N are disjoint set.
Representing the set in Venn diagram;
