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;