In this chapter we will learn to represent union of sets using Venn diagram with examples.

Let’s first review the union operation in set theory.

## What is Union in set theory ?

If A & B are two sets, then union operation will result in element present in both set A & B.

For Example;

If A = { 3, 5, 7 }

B = {2, 4, 7, 8 }

Then, A union B = {2, 3, 4, 5, 7, 8}

### Symbol of Union of Set

The union operation is represented by symbol **” ∪ “**.

So, if we want to perform union of set A & B, we will represent as ” A ∪ B “

### Union of Set – General Expression

In set builder form, the union of set A & B can be represented as follows;**A ∪ B = { x : x 𝜖 A or x 𝜖 B }**

It says that A union B consist of entity x, where x belongs to either set A or B.

## Using Venn diagram in Union Operation

If you want to understand the **basics of Venn diagram in set theory**, please click the link.

You can use Venn diagram to graphically represent union operation between two or more sets.

If A & B are two sets, the Venn diagram diagram representation is shown below.

In the above image;

(a) **Rectangular box** represent** universal set**.

(b)** Circle A & B** represent the **set A & B **respectively.

(c) The** green color represent the union of sets** which covers all the element present both in set A & B.

i hope you understood the basic concept, let us now look at the properties of union of set with Venn diagram.

## Important Union Property & Operation with Venn diagram

(01)** If A ⊆ B, then A ⋃ B = B**

It says that if A is subset of B, then union of set A & B will result in set B.

In the above image;

⟹ rectangle represents the universal set

⟹ big circle represent set B and small circle represent set A.

Since A is subset of B, all the elements of set A are present in set B. That’s why circle A is present inside circle B.

⟹ The union of A ⋃ B results in set B which is shown by green color.

**(02) A ∪ B = B ∪ A **

In the union operation, if we change the order of set, we will get the same result.

(03)** A ⋃ A’ = Universal set **

The union of set A with its complement will result in universal set.

In the above image;

⟹ Set A is represented by orange color

⟹ Set A’ (Set A compliment) is represented by pink color

⟹ the union of A ⋃ A’ results in complete rectangle box shown by blue color

(04)** A ⋃ B’ **

Here we are doing union of set A with B complement.

In the first Image;

⟹ Set A is shown by green color

⟹ Set B’ is shown by pink color

After taking union of A ⋃ B’ we get the second image.

Here the blue color represent the solution A ⋃ B’