How to Draw a Four Circle Venn Diagram

Venn Diagram

A Venn diagram is used to visually correspond the differences and the similarities between ii concepts. Venn diagrams are also called logic or gear up diagrams and are widely used in set up theory, logic, mathematics, businesses, teaching, informatics, and statistics.

Allow's larn about Venn diagrams, their definition, symbols, and types with solved examples.

1.	What is a Venn Diagram?
2.	Venn Diagram Symbols
3.	Venn Diagram for Set Operations
4.	Venn Diagram for Three Sets
five.	How to Draw a Venn Diagram?
6.	Applications of Venn Diagrams
7.	FAQs on Venn Diagram

What is a Venn Diagram?

A Venn diagram is a diagram that helps us visualize the logical human relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may exist used) to denote the relationship between sets.

Venn Diagram Example

Permit us observe a Venn diagram instance. Here is the Venn diagram that shows the correlation between the following set of numbers.

• One set contains fifty-fifty numbers from 1 to 25 and the other gear up contains the numbers in the 5x tabular array from 1 to 25.
• The intersecting function shows that x and xx are both even numbers and likewise multiples of v between ane to 25.

Terms Related to Venn Diagram

Permit the states understand the following terms and concepts related to Venn Diagram, to understand information technology better.

Universal Set

Whenever we utilize a set up, information technology is easier to commencement consider a larger prepare called a universal set that contains all of the elements in all of the sets that are being considered. Whenever we depict a Venn diagram:

• A large rectangle is used to represent the universal prepare and it is usually denoted by the symbol E or sometimes U.
• All the other sets are represented by circles or airtight figures inside this larger rectangle.
• Every fix is the subset of the universal set U.

Consider the higher up-given image:

• U is the universal gear up with all the numbers one-ten, enclosed within the rectangle.
• A is the set up of even numbers one-10, which is the subset of the universal set U and it is placed inside the rectangle.
• All the numbers between one-ten, that are not even, volition exist placed outside the circle and inside the rectangle equally shown above.

Subset

Venn diagrams are used to show subsets. A subset is actually a set that is contained inside another set. Let united states of america consider the examples of two sets A and B in the beneath-given figure. Here, A is a subset of B. Circle A is contained entirely within circle B. Besides, all the elements of A are elements of fix B.

This human relationship is symbolically represented as A ⊆ B. It is read equally A is a subset of B or A subset B. Every fix is a subset of itself. i.e. A ⊆ A. Hither is another example of subsets :

• North = ready of natural numbers
• I = prepare of integers
• Here N ⊂ I, considering all-natural numbers are integers.

Venn Diagram Symbols

In that location are more xxx Venn diagram symbols. We will larn about the three most ordinarily used symbols in this department. They are listed below as:

Venn Diagram Symbols	Caption
The wedlock symbol - ∪	A ∪ B is read equally A union B. Elements that vest to either ready A or set B or both the sets. U is the universal set.
The intersection symbol - ∩	A ∩ B is read as A intersection B. Elements that vest to both sets A and B. U is the universal set.
The complement symbol - Ac or A'	A' is read as A complement. Elements that don't belong to set A. U is the universal set.

Let the states understand the concept and the usage of the three basic Venn diagram symbols using the image given below.

Symbol	Information technology refers to	Full Elements (No. of students)
A ∪ C	The number of students that prefer either burger or pizza or both.	1 + 10 + 2 + 2 + 6 + 9 = thirty
A ∩ C	The number of students that prefer both burger and pizza.	2 + ii = 4
A ∩ B ∩ C	The number of students that prefer a burger, pizza as well as hotdog.	ii
Ac or A'	The number of students that do not prefer a burger.	10 + half dozen + 9 = 25

Venn Diagram for Sets Operations

In fix theory, we tin can perform sure operations on given sets. These operations are equally follows,

• Marriage of Set
• Intersection of set
• Complement of ready
• Difference of set

Spousal relationship of Sets Venn Diagram

The union of two sets A and B can be given past: A ∪ B = {x | ten ∈ A or x ∈ B}. This performance on the elements of gear up A and B tin be represented using a Venn diagram with ii circles. The total region of both the circles combined denotes the matrimony of sets A and B.

Intersection of Set Venn Diagram

The intersection of sets, A and B is given by: A ∩ B = {x : x ∈ A and x ∈ B}. This operation on set A and B can exist represented using a Venn diagram with 2 intersecting circles. The region common to both the circles denotes the intersection of set A and Set B.

Complement of Ready Venn Diagram

The complement of any set A tin exist given as A'. This represents elements that are not present in set A and tin can exist represented using a Venn diagram with a circle. The region covered in the universal set, excluding the region covered by fix A, gives the complement of A.

Deviation of Prepare Venn Diagram

The divergence of sets can be given equally, A - B. It is also referred to as a 'relative complement'. This functioning on sets can be represented using a Venn diagram with two circles. The region covered by set A, excluding the region that is common to set B, gives the deviation of sets A and B.

We can observe the above-explained operations on sets using the figures given below,

Venn Diagram for Three Sets

3 sets Venn diagram is made up of 3 overlapping circles and these three circles show how the elements of iii sets are related. When a Venn diagram is made of iii sets, it is besides called a 3-circle Venn diagram. In a Venn diagram, when all these three circles overlap, the overlapping parts contain elements that are either mutual to whatsoever two circles or they are common to all the three circles. Let the states consider the beneath given case:

Hither are some important observations from the above image:

• Elements in P and Q = elements in P and Q only plus elements in P, Q, and R.
• Elements in Q and R = elements in Q and R just plus elements in P, Q, and R.
• Elements in P and R = elements in P and R only plus elements in P, Q, and R.

How to Draw a Venn Diagram?

Venn diagrams tin be drawn with unlimited circles. Since more three becomes very complicated, we will commonly consider only two or 3 circles in a Venn diagram. Hither are the four like shooting fish in a barrel steps to describe a Venn diagram:

• Footstep ane: Categorize all the items into sets.
• Step ii: Describe a rectangle and label it as per the correlation between the sets.
• Step 3: Draw the circles according to the number of categories y'all have.
• Pace 4: Place all the items in the relevant circles.

Example: Permit us draw a Venn diagram to bear witness categories of outdoor and indoor for the following pets: Parrots, Hamsters, Cats, Rabbits, Fish, Goats, Tortoises, Horses.

• Footstep i: Categorize all the items into sets (Here, its pets): Indoor pets: Cats, Hamsters, and, Parrots. Outdoor pets: Horses, Tortoises, and Goats. Both categories (outdoor and indoor): Rabbits and Fish.
• Stride 2: Describe a rectangle and label it as per the correlation between the 2 sets. Hither, allow'due south characterization the rectangle every bit Pets
• Step three: Draw the circles according to the number of categories you have. There are two categories in the sample question: outdoor pets and indoor pets. So, let us draw 2 circles and make sure the circles overlap.

• Step 4: Identify all the pets in the relevant circles. If there are certain pets that fit both the categories, then place them at the intersection of sets, where the circles overlap. Rabbits and fish can exist kept as indoor and outdoor pets, and hence they are placed at the intersection of both circles.

• Footstep 5: If there is a pet that doesn't fit either the indoor or outdoor sets, and then place it within the rectangle but outside the circles.

Applications of Venn Diagram

There are several advantages to using Venn diagrams. Venn diagram is used to illustrate concepts and groups in many fields, including statistics, linguistics, logic, education, computer scientific discipline, and business.

• We can visually organize information to come across the relationship betwixt sets of items, such as commonalities and differences, and to depict the relations for visual communication.
• We can compare 2 or more subjects and clearly see what they accept in common versus what makes them different. This might be done for selecting an important product or service to buy.
• Mathematicians also use Venn diagrams in math to solve complex equations.
• We can employ Venn diagrams to compare data sets and to find correlations.
• Venn diagrams tin be used to reason through the logic behind statements or equations.

☛ Related Articles:

Check out the following pages related to Venn diagrams:

• Operations on Sets
• Roster Notation
• Set Builder Note
• Statistics
• Probability

Important Notes on Venn Diagrams

Here is a list of a few points that should be remembered while studying Venn diagrams:

• Every set is a subset of itself i.due east., A ⊆ A.
• A universal fix accommodates all the sets under consideration.
• If A ⊆ B and B ⊆ A, so A = B
• The complement of a complement is the given set itself.

Venn Diagram Examples

1. Case 1: Let the states take an example of a gear up with diverse types of fruits, A = {guava, orange, mango, custard apple, papaya, watermelon, ruddy}. Represent these subsets using sets annotation: a) Fruit with one seed b) Fruit with more than than one seed

   Solution: Amidst the diverse types of fruit, but mango and cherry have ane seed.

   Thus,

   1. Fruit with one seed = {mango, reddish}
   2. Fruit with more one seed = {guava, orange, custard apple, papaya, watermelon}

2. Case two: Permit united states have an example of 2 sets A and B, where A = {3, 7, ix} and B = {iv, eight}. These ii sets are subsets of the universal set U = {1, ii, 3, 4, v, half-dozen, 7, eight, nine}. Find A ∪ B.

   Solution: The Venn diagram for the to a higher place relations tin can be fatigued as:

   

   A ∪ B means, all the elements that belong to either set up A or set B or both the sets = {iii, 4, 7, viii, 9}

3. Example 3: Using Venn diagram, discover X ∩ Y, given that X = {one, 3, 5}, Y = {2, 4, vi}.

   Solution:

   Given: X = {one, iii, 5}, Y = {2, four, 6}

   The Venn diagram for the above example tin can be given as,

   

   From the Venn diagram, nosotros observe that, 10 ∩ Y = ∅.

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Venn Diagram Exercise Questions

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FAQs on Venn Diagrams

What is a Venn Diagram in Math?

In math, a Venn diagram is used to visualize the logical human relationship between sets and their elements and helps the states solve examples based on these sets.

How practice You Read a Venn Diagram?

These are steps to be followed while reading a Venn diagram:

• Offset, observe all the circles that are present in the entire diagram.
• Every element nowadays in a circumvolve is its ain item or data set.
• The intersecting or the overlapping portions of the circles contain the items that are common to the different circles.
• The parts that do non overlap or intersect show the elements that are unique to the different circle.

What is the Importance of Venn Diagram?

Venn diagrams are used in unlike fields including business organization, statistics, linguistics, etc. Venn diagrams can be used to visually organize information to run across the relationship between sets of items, such as commonalities and differences, and to draw the relations for visual advice.

What is the Center of a Venn Diagram Called?

When 2 or more sets intersect, overlap in the middle of a Venn diagram, it is called the intersection of a Venn diagram. This intersection contains all the elements that are common to all the different sets that overlap.

How to Represent a Universal Fix Using Venn Diagram?

A large rectangle is used to correspond the universal set and information technology is usually denoted past the symbol E or sometimes U. All the other sets are represented by circles or closed figures within this larger rectangle that represents the universal set.

What are the Different Types of Venn Diagrams?

The different types of Venn diagrams are:

• Two-set Venn diagram: The simplest of the Venn diagrams, that is fabricated upwards of two circles or ovals of different sets to show their overlapping properties.
• Iii-set Venn diagram: These are also called the three-circle Venn diagram, as they are made using three circles.
• Four-set Venn diagram: These are made out of four overlapping circles or ovals.
• Five-set Venn diagram: These comprise of five circles, ovals, or curves. In gild to make a five-set up Venn diagram, you lot can besides pair a 3-set diagram with repeating curves or circles.

What are the Unlike Fields of Applications of Venn Diagrams?

There are dissimilar cases of applications of Venn diagrams: Set theory, logic, mathematics, businesses, teaching, computer science, and statistics.

Can a Venn Diagram Have three Circles?

Yep, a Venn diagram tin have three circles, and information technology'southward chosen a three-set Venn diagram to show the overlapping properties of the three circles.

What is Wedlock in the Venn Diagram?

A union is 1 of the basic symbols used in the Venn diagram to prove the relationship between the sets. A union of two sets C and D can be shown as C ∪ D, and read equally C union D. It means, the elements belong to either gear up C or set D or both the sets.

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Source: https://www.cuemath.com/algebra/venn-diagram/

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