## Venn DiagramIn mathematics, the In this section, we will learn that A set is a collection or group of things. It may contain digits, vowels, animals, prime numbers, etc. A set is denoted by the capital letter and the elements of the set are denoted by the lowercase letters. All the elements of a set enclose in the pair of curly braces {}. For example,
Where E is the set name and 2, 4, 6, 8 are the elements of the set. We can also represent a set-in pictorial form that is known as ## What is the Venn diagram?A diagram or figure that represents the mathematical logic or relation between a finite collection of different sets (a group of things) is called the Suppose there are two sets A and B having the elements {1, 2, 3} and {8, 5, 9}, respectively. We can represent these two sets in the Venn diagram, as shown below. ## Advantages of Venn Diagram- It is used for both comparison and classification.
- It groups the information into different parts.
- It also highlights the similarities and differences.
## Uses of Venn DiagramVenn diagram is used in mathematics to understand the set theory. We also use it to understand the relationship between or among sets of objects. It depicts the set of intersections and unions. ## How to Draw a Venn Diagram- First, we draw a rectangle.
- Write the
**union**() sign either the left or right top corner of the rectangle. - Inside the rectangle, write the elements that do not belong to any set. Draw circle(s) that represent the set.
- Inside or outside of the circle, write the name of the corresponding set.
- Inside the circle, write the elements of the set.
Suppose there are two sets, A and B, having some elements in common. The Venn diagram of the sets can be drawn as follows: ## Types of Venn DiagramThere are following types of Venn diagram: - Two-Set Diagrams
- Two-Set Euler Diagrams
- Three-Set Diagrams
- Three-Set Euler Diagrams
- Four-Set Diagrams
If a set is completely encompassing the other set, it is both the Euler diagram and the Venn diagram. Suppose a set A represents the set of animals and set B represents the set of carnivorous animals. It is clear that all the animals cannot be carnivorous, but vice-versa is true. Therefore, all the carnivorous animals also present in the set of animals, i.e., A. We can represent it in the Venn diagram, as follows.
**David**is the student who learns both**physics**and**math**.**Michael**is the student who learns both**chemistry**and**math**.**Sam**is the student who learns both**chemistry**and**physics**.**Tom**is the student who learns three-subject**chemistry, math,**and**physics**.
Therefore, we can represent it in the Venn diagram, as shown below.
The three-set Euler diagram can have a nested set. In the following diagram, the pink things set may contain a set of light-pink things. The above diagram is not a Venn diagram because two sets do not overlap (Black Things & light-pink Things) each other.
We also use a three-set diagram with a curve to represent the four-set diagram. When a four-set diagram that uses circles will also be a Euler diagram, the circle would not show the union between every pair of sets. Before moving to example, let's have a quick view of the symbols used in set theory.
Let's solve some examples based on the Venn diagram.
**The number of employees likes only tea?****The number of employees likes only green tea?****The number of employees likes neither tea nor green tea?****The number of employees likes only one of tea or green tea?****The number of employees likes at least one of the beverages?**
- Number of employees who like only tea =
**60** - Number of employees who like only green tea =
**40** - Number of employees who like neither tea nor green tea =
**20** - Number of employees who like only one of tea or green tea = 60 + 40 =
**100** - Number of employees who like at least one of tea or green tea = n (only Tea) + n (only green tea) + n (both Tea & green tea) = 60 + 40 + 80 =
**180**
**49% of students liked to play football.****53% of students liked to play hockey.****62% of students liked to play basketball.****27% of students liked to play both football and hockey.****29% of students liked to play both basketball and hockey.****29% of students liked to play both football and basketball.****5% of students do not like to play any game.**
**The percentage of students who like to play all the games?****Find the ratio of the percentage of students who like to play only football for those who like to play only hockey.****The percentage of students who like to play only one game.****The percentage of students who like to play at least two games.**
n(F) = students who like to play football = 49% Since, 5% like to play none of the given games so, n (F ∪ H ∪ B) = 95%. Now applying the basic formula, 95% = 49% + 53% + 62% -27% - 29% - 28% + n (F ∩ H ∩ B) Solving, we get n (F ∩ H ∩ B) = 15%. Now, we will draw the Venn diagram based on the information that we have calculated. Remember that all the values in the diagram are in percentages. Next TopicCompound Interest |