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

From Difference of Sets using Venn Diagram to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More