In this chapter we will learn to represent set difference operation using Venn diagram.

Let’s first review the basics of set difference operation.

## What is Difference of set ?

Let there are two sets A & B.

The difference of** set A – B** will result in** elimination of common elements of set A & B from set A**.

**For example**;

Let A = { 3, 6, 9, 12, 15 }

B = { 8, 9, 10, 11, 12 }

Note that between set A & B, the numbers 9 & 12 are common elements.

So in A – B operation, the common elements 9 & 12 will be removed from set A.

Hence, A – B = {3, 6, 15}

### Representation of difference of sets

The difference between two sets are represented by symbol **” – “**

If there are two sets A & B then there are two possibilities of set difference;**(a) A – B**

In this operation, the common elements will be removed from set A.**(b) B – A**

In this operation, the common elements will be removed from set B.

## Using Venn diagram in set difference

To learn basics of **Venn diagram in set theory,** click the red link.

The set difference operation can be presented graphically with the help of Venn diagram.

Representing A – B in Venn diagram

Consider the two sets A & B, the difference of set A – B is shown by below image.

In the above image;

⟹ rectangular box represent universal set

⟹ Circle A & B represent set A & B respectively

⟹ The area in blue color represent the set difference A – B.

**Important Points:**

(a) In operation A – B, we have removed common elements of A & B from set A.

(b) The set A – B only contain unique elements of A.

### Representing B – A in Venn diagram

The Venn diagram representation of B – A is shown below;

In the above image;

⟹ The green area represent the difference of set B – A

⟹ Here we are subtracting common elements of set A & B from set B.

## Examples of Set difference with Venn diagram

**(01) Given below are sets A & B. Represent A – B and B – A using Venn diagram.**

A = { 1, 3, 5, 7, 9, 11 }

B = { 2, 3, 5, 7, 8 }

**Solution**

In set A & B, the common elements are 3, 5, & 7 **Solving for A – B**

In this operation we will remove common elements A & B from set A.

A – B = { 1, 9, 11 }

Venn diagram representation of A – B.

The area colored in grey represents A – B.

**Solving for B – A**

Here we will remove common elements of A & B from set B.

B – A = { 2 , 8 }

Venn diagram representation;

The green area represent B – A

**(02) Represent P – Q in Venn diagram.**

P = { Monday, Tuesday, Wednesday }

Q ={ Wednesday, Thursday, Friday }

**Solution**

In both set P & Q, the term ” Wednesday ” is the common element.

**Solving for P – Q**

In operation P – Q, we will eliminate common elements of P & Q from set P.

P – Q = { Monday, Tuesday }

(03) Given below are set A, B & C.

A = { 2, 3, 4 }

B = { 4, 5, 6 }

C = {2, 4, 7 }

Find the following operation;

(a) A – B

(b) B – A

(c) B – C

(d) C – A

**Solution****(a) Solving for A – B**

A – B = { 2, 3 }

Yellow area represent operation A – B.

**(b) Solving for B – A**

B – A = { 5, 6 }

The pink area represent set B – A.

**(c) Solving for B – C**

B – C = { 5, 6 }

The grey area represent set B – C.

**(d) Solving for C – A**

Here number 2 & 4 are common between set C & A

C – A = { 7 }

The green area represent the set C – A.