Difference of Sets using Venn Diagram

How to find the difference of sets using Venn diagram?

The difference of two subsets A and B is a subset of U, denoted by A – B and is defined by 

A – B = {x : x ∈ A and x ∉ B}.

Let A and B be two sets. The difference of A and B, written as A - B, is the set of all those elements of A which do not belongs to B.

Thus A – B = {x : x ∈ A and x ∉ B} or A – B = {x ∈ A : x ∉ B}.

Clearly, x ∈ A – B

⇒ x ∈ A and x ∉ B

In the adjoining figure the shaded part represents A – B.

Difference of Sets using Venn Diagram

Similarly, the difference B – A is the set of all those elements of B that do not belongs to A.

Thus, B – A = {x : x ∈ A and x ∉ B} or A – B = {x ∈ B : x ∉ A}.

In the adjoining figure the shaded part represents B – A.

Difference of Sets Venn Diagram

In particular, A – B = ∅ if A ⊂ B and A – B = A if A ∩ B = ∅.

The subset of A – B is also called the complement of B relative to A.

The difference A – B can be expressed in terms of the complement as A – b = A ∩ B’.

Properties of difference of sets:

1. A – (B ∩ C) = (A – B) ∪ (A – C)

2. A – (B ∪ C) = (A – B) ∩ (A – C)


Solved example to find the difference of sets using Venn diagram:

1. If A = {2, 3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}, then find (i) A – B and (ii) B – A.

Solution:

According to the given statement; A = {2, 3, 4, 5, 6, 7} and B = {3, 5, 7, 9, 11, 13}

(i) A – B

Difference of Sets

= {2, 4, 6}


(ii) B – A

Difference of Two Sets

= {9, 11, 13}


2. Given three sets A, B and C such that: A = {x : x is a natural number between 10 and 16}, B = {set of even numbers between 8 and 20} and C = {7, 9, 11, 14, 18, 20}.

Find the difference of sets using Venn diagram:

(i) A – B

(ii) B – C

(iii) C – A

(iv) B – A

Solution:

According to the given statement

A = {11, 12, 13, 14, 15}

B = {10, 12, 14, 16, 18}

C = {7, 9, 11, 14, 18, 20}


(i) A – B

Shaded Part Represents B – A

= {Those elements of set A which are not in set B}

= {11, 13, 15}


(ii) B – C

Difference of Set A and Set B

= {Those elements of set B which are not in set C}

= {10, 12, 16}


(iii) C – A

Find the Difference of Sets

= {Those elements of set C which are not in set A}

= {7, 9, 18, 20}


(iv) B – A

Difference of Sets Example

= {Those elements of set B which are not in set A}

= {10, 16, 18}

Set Theory

Sets Theory

Representation of a Set

Types of Sets

Finite Sets and Infinite Sets

Power Set

Problems on Union of Sets

Problems on Intersection of Sets

Difference of two Sets

Complement of a Set

Problems on Complement of a Set

Problems on Operation on Sets

Word Problems on Sets

Venn Diagrams in Different Situations

Relationship in Sets using Venn Diagram

Union of Sets using Venn Diagram

Intersection of Sets using Venn Diagram

Disjoint of Sets using Venn Diagram

Difference of Sets using Venn Diagram

Examples on Venn Diagram



8th Grade Math Practice

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