**What is Difference of sets?**

If A & B are given two sets, then the** difference of set A & B will results in**:

⟹ removal of common element between A & B from set A

⟹ only the unique element of set A will remain after subtraction.

**For Example**

Given below are sets A & B; Do the subtraction A – B.

In the operation the main set A is subtracted with set B.

To find the subtraction we have to remove the common elements of A & B from set A.

Note that elements 7 & 15 are the common elements between A & B.

The subtraction of sets A – B will;

⟹ remove common elements 7 & 15 from set A

⟹ only the unique elements of set A will be left.

Hence, the elements in set A – B are;

**Conclusion**

In difference of sets, the common elements are removed from the main set.

**Representing Set Difference**

The difference between two sets in represented by symbol ” – “.

Hence, the difference of two sets A & B is represented as:

It means that set A is subtracted with set B.

In this operation we have to subtract the common elements of A & B from main set A.

Similarly the subtraction of set B with A is expressed as;

In this operation we have to remove common elements of A & B from main set B.

**Representing set difference through Venn diagram**

Venn diagram is useful for graphical representation of different sets.

In Venn diagram, the sets are represented through circles and universal set is represented by rectangular box.

Consider two sets A & B with following elements;

A = { 1, 5, 9, 15, 17 }

B = { 5, 10, 15, 20 }

Given below is the Venn diagram for subtraction of set A – B.

The **area covered in green represents the set A – B**.

Note that the green area only contain the element which is unique to set A.

The common elements ( i.e. 5 & 15 ) have been removed from the difference operation.

Hence, A – B = { 1, 9, 17 }

**Solved Questions on Set Difference**

(01) Given below are two sets A & B

Find A – B and B – A

**Solution**

Finding A – B

Here we have to subtract common elements of A & B from set A.

Note that elements 13, 15 & 17 are the common elements in set A & B.

**A – B = { 19, 22, 25 }**

**Finding B – A**

Subtract common elements of B & A from set B.

Again elements 13, 15 & 17 are the common elements in A & B.

**B – A = { 5, 8, 20 }**

**(02) Given below are two sets A, B and C**

Find;

( i ) A – B

( ii ) B – A

( iii ) C – A

( iv ) A – C

( v ) B – C

**Solution**

Let us first write all the sets in Roster form.

A = { x : x is greater than 15 and less than 25 }

Roster form of set A is;

A = { 16, 17, 18, 19, 20, 21, 22, 23, 24 }

B = { x : x is greater than 10 & less than 17 }

Roster form of set B is;

B = { 11, 12, 13, 14, 15, 16}

Hence, all the three sets in Roster form are;

A = { 16, 17, 18, 19, 20, 21, 22, 23, 24 }

B = { 11, 12, 13, 14, 15, 16}

C = { 11, 14, 17, 19, 23}

**( i ) A – B**

Number 16 is the only common element between A & B.

Removing the common element between A & B from set A we get;

A – B = { 17, 18, 19, 20, 21, 22, 23, 24}

**( ii ) B – A**

Again 16 is the common element between A & B.

Removing 16 from set B we get;

B – A = { 11, 12, 13, 14, 15}

**( iii ) C – A**Number 17, 19 & 23 are the common element between set A & C.

Removing 17, 19 & 23 from set C we get;

C – A = { 11, 14 }

**( iv ) A – C**

Again number 17, 19 & 23 are the common elements between set A & C.

Removing common elements from set A.

A – C = { 16, 18, 20, 21, 22, 24 }

**( v ) B – C**

Number 11 & 14 are the common elements between set A & C.

Remove common elements from set B & C.

B – C = { 12, 13, 15, 16 }

**(03) Given below are two sets A & B.**

A = { Orange, Banana, Apple, Cherry }

B = { Mango, Banana, Strawberry, Guava, Cherry }

Find A – B and B – A

**Solution****(i) A – B**

Here Banana and Cherry are the common elements between set A & B.

Remove the common elements from set A , we get;

A – B = { Orange, Apple }

**(ii) B – A**

Remove the above mentioned common elements from set B, we get;

B – A = { Mango, Strawberry, Guava }

**(04) Given below are two sets A & B**

Find A – B

**Solution**

Let us first write the set A in Roster form

A = { x : x lies between 6 & 10 }

Set A can also be written as;

A = { 7, 8, 9 }

Hence, the two given sets in roster form are;

A = { 7, 8, 9 }

B = { 𝜙 }

Note that there is no common element between set A & B.

So no element will be removed from set A.

Hence, A – B = { 7, 8, 9 }