Venn Diagram Of Real Numbers

Venn diagrams are the diagrams that are used to stand for the sets, relation between the sets and operation performed on them, in a pictorial fashion. Venn diagram, introduced by John Venn (1834-1883), uses circles (overlapping, intersecting and not-intersecting), to denote the human relationship betwixt sets. A Venn diagram is also called a prepare diagram or a logic diagram showing different set operations such as the intersection of sets, union of sets and deviation of sets. It is likewise used to draw subsets of a set.

For example, a set of natural numbers is a subset of whole numbers, which is a subset of integers. The relation betwixt the sets of natural numbers, whole numbers and integers tin can be shown past the Venn diagram, where the set of integers is the universal set.  See the figure below.

Here, W represents whole numbers and Due north represents natural numbers

The universal set (U) is usually represented past a airtight rectangle, consisting of all the sets. The sets and subsets are shown by using circles or oval shapes.

Tabular array of Contents:

• Definition
• Symbols
• How to Describe
• Operations
  • Complement
  • Intersection
  • Union
  • Complement of Matrimony
  • Complement of Intersection
  • Deviation
  • Symmetric Difference
• Example
• FAQs

What is a Venn Diagram?

A diagram used to represent all possible relations of different sets. A Venn diagram tin be represented by whatever closed figure, whether information technology be a Circumvolve or a Polygon (square, hexagon, etc.). But usually, we use circles to represent each fix.

In the above figure, we can run into a Venn diagram, represented by a rectangular shape about the universal set, which has 2 independent sets, X and Y. Therefore, X and Y are disjoint sets. The two sets, X and Y, are represented in a circular shape. This diagram shows that set X and set Y have no relation between each other, merely they are a part of a universal set.

For case, prepare 10 = {Set of even numbers} and set Y = {Gear up of odd numbers} and Universal set, U = {set of natural numbers}

Nosotros tin use the below formula to solve the bug based on two sets.

northward(X ⋃ Y) = north(10) + north(Y) – n(X ⋂ Y)

Venn Diagram of Iii Sets

Check the Venn diagram of three sets given below.

The formula used to solve the problems on Venn diagrams with three sets is given beneath:

northward(A ⋃ B ⋃ C) = n(A) + n(B) + northward(C) – n(A ⋂ B) – n(B ⋂ C) – n(A ⋂ C) + north(A ⋂ B ⋂ C)

Venn Diagram Symbols

The symbols used while representing the operations of sets are:

• Spousal relationship of sets symbol: ∪
• Intersection of sets symbol: ∩
• Complement of set: A' or A^c

How to draw a Venn diagram?

To describe a Venn diagram, get-go, the universal set should be known. Now, every set is the subset of the universal set (U). This means that every other gear up will exist inside the rectangle which represents the universal set up.

So, any set A (shaded region) will be represented as follows:

Figure ane:

Where U is a universal fix.

Nosotros can say from fig. ane that

A ∪ U = U

All the elements of set A are within the circle. As well, they are office of the big rectangle which makes them the elements of set up U.

Venn Diagrams of Set operations

In set theory, there are many operations performed on sets, such as:

• Union of Fix
• Intersection of set up
• Complement of set
• Difference of set

etc. The representations of dissimilar operations on a set are as follows:

Complement of a fix in Venn Diagram

A' is the complement of ready A (represented by the shaded region in fig. two). This fix contains all the elements which are not in that location in set A.

Effigy 2:

It is clear that from the above effigy,

A + A' = U

It means that the prepare formed with elements of set A and set up A' combined is equal to U.

(A')'= A

The complement of a complement gear up is a set itself.

Properties of Complement of ready:

• A ∪ A′ = U
• A ∩ A′ = φ
• (A ∪ B)′ = A′ ∩ B′
• (A ∩ B)′ = A′ ∪ B′
• U′ = φ
• φ′ = U

Intersection of two sets in Venn Diagram

A intersection B is given by: A ∩ B = {x : 10 ∈ A and x ∈ B}.

This represents the mutual elements betwixt set A and B (represented by the shaded region in fig. iii).

Figure 3:

Intersection of two Sets

Backdrop of the intersection of sets operation:

• A ∩ B = B ∩ A
• (A ∩ B) ∩ C = A ∩ (B ∩ C)
• φ ∩ A = φ ; U ∩ A = A
• A ∩ A = A
• A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
• A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

Wedlock of Two Sets in Venn Diagram

A union B is given by:A ∪ B = {ten | x ∈A or x ∈B}.

This represents the combined elements of set A and B (represented by the shaded region in fig. iv).

Figure four:

Union of two sets

Some properties of Union functioning:

• A ∪ B = B ∪ A
• (A ∪ B) ∪ C = A ∪ (B ∪ C)
• A ∪ φ = A
• A ∪ A = A
• U ∪ A = U

Complement of Union of Sets in Venn Diagram

(A ∪ B)': This is read as complement of A wedlock B. This represents elements which are neither in set A nor in ready B (represented past the shaded region in fig. v).

Figure five:

Complement of A U B

Complement of Intersection of Sets in Venn Diagram

(A ∩ B)': This is read as complement of A intersection B. This represents elements of the universal set which are not common betwixt ready A and B (represented by the shaded region in fig. six).

Effigy 6:

Complement of A ∩ B

Deviation between Two Sets in Venn Diagram

A – B: This is read as A divergence B. Sometimes, it is also referred to as 'relative complement'. This represents elements of set A which are not there in gear up B(represented by the shaded region in fig. 7).

Figure 7:

Departure between Two Sets

Symmetric deviation betwixt two sets in Venn Diagram

A ⊝ B: This is read as asymmetric departure of set A and B. This is a set which contains the elements which are either in set A or in ready B only non in both (represented past the shaded region in fig. 8).

Effigy 8:

Symmetric difference between 2 sets

Related Articles

• Sets
• Set Theory in Maths
• Set Operations
• Subset And Superset
• Intersection And Difference Of 2 Sets

Venn Diagram Example

Instance: In a class of 50 students, 10 have Guitar lessons and twenty take singing classes, and 4 take both. Find the number of students who don't accept either Guitar or singing lessons.

Solution:

Let A = no. of students who take guitar lessons = x.

Allow B = no. of students who take singing lessons = twenty.

Let C = no. of students who accept both = 4.

At present we subtract the value of C from both A and B. Allow the new values exist stored in D and E.

Therefore,

D = 10 – 4 = 6

E = 20 – 4 = 16

Now logic dictates that if we add the values of C, D, East and the unknown quantity "X", we should get a total of fifty right? That's right.

So the final answer is X = 50 – C – D – E

10 = l – 4 – 6 – 16

Ten = 24 [ Answer]

Venn's diagrams are particularly helpful in solving word issues on number operations that involve counting. Once it is drawn for a given problem, the rest should exist a easy.

Venn Diagram Questions

1. Out of 120 students in a schoolhouse, 5% can play Cricket, Chess and Carroms. If so happens that the number of players who can play whatever and only two games are 30. The number of students who tin can play Cricket solitary is 40. What is the full number of those who can play Chess alone or Carroms solitary?
2. Draw the diagram that best represents the relationship among the given classes:
   Fauna, Tiger, Vehicle, Car
3. At an overpriced department shop, there are 112 customers. If 43 have purchased shirts, 57 take purchased pants, and 38 take purchased neither, how many purchased both shirts and pants?
4. In a group, 25 people like tea or java; of these, 15 similar tea and 6 like coffee and tea. How many like coffee?

To learn more than from sets and other topics, download BYJU'S – The Learning App and explore the visual power of learning.

Frequently Asked Questions on Venn Diagram

What practice yous mean past venn diagram?

Venn diagram is a diagram used to stand for all possible relations of dissimilar sets.

How do Venn diagrams piece of work?

A Venn diagram is an analogy that uses circles to showroom the relationships among things or finite groups of items. Circles that overlap have a commonality, while circles that do non overlap practise not share those attributes. Thus, Venn diagrams help to depict the similarities and differences between the given concepts visually.

How do you do Venn diagrams in math?

In maths, Venn diagrams are used to represent the human relationship between ii or more sets. This way of expressing sets or certain situations helps in improve understanding the scenario to conclude hands. Thus, we generally use circles to exhibit the relationships amid things or finite groups of items.

What does A ∩ B mean?

In mathematics, the intersection of ii sets A and B, denoted by A ∩ B, contains all elements of A that besides vest to B (or equivalently, all elements of B that also belong to A).

What are the different types of Venn diagrams?

The Venn diagram types are defined based on the number of sets or circles involved in the Universal set or the rectangular space. They are:
Two-set Venn diagram
Three-ready Venn diagram
Four-set Venn diagram
5-ready Venn diagram

What are the four benefits of using Venn diagrams?

The 4 benefits of using Venn diagrams include the following:
These are used for the nomenclature and comparison of two things.
Different parameters can be obtained without much adding, such equally intersection, union, difference, etc.
Due to its pictorial representation, one can understand the given situation chop-chop.
These will make the complex calculation much simpler that involves sets.

Venn Diagram Of Real Numbers,

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