What is a Venn Diagram

What is Set?

In our daily lives we see so many things around us: clothes, shoes, food, animals, birds, people and so on. All these things around us can be placed in groups. For example: a group of fruits, a group of vegetables, a group of pants, a group of girls etc. This grouping and collection of things, in mathematical terms, is known as a set. These sets can be used to show the relationships between two or three groups. Sets are used to illustrate a logical relationship between groups. For example: A set of whole numbers: {0, 1, 2, 3….} or a set of the names of boys in a class: {John, Jimmy, Alex, Sam, Brad}.

Examples of Sets

Let us see the relationship between two sets. For example: A set of girls playing tennis {Ritu, Tanu, Anita, Sita} and a set of girls playing Basketball {Tanu, Sonal, Anita, Meera}. A set of girls playing Tennis or Basketball is: Tennis Union Basketball {Ritu, Tanu, Anita, Sita, Sonal, Meera}

From these two sets we can see that there are some girls who play both- tennis and basketball. Thus we can make a new set: Tennis Intersection Basketball {Tanu, Anita}.

Venn Diagram : Definition

Sets can be easily understood and represented by a Venn diagram. Venn diagrams are graphical or pictorial representation of relationships between different groups of things. They were invented by John Venn around 1880. Venn diagrams are also called set diagrams. Venn diagrams give a logical representation of the groups or sets. Relationships between two or three sets can be easily understood with the help of Venn diagrams.

How to draw a Venn Diagram?

Step 1 : Draw a rectangle. This is known as the ‘Universe’. Here the Universe is everything that a set is dealing with. For example, if you are dealing with a set of games like Basketball, Football, Hockey, Table Tennis, Badminton, Cricket, Chess and Video games then ‘Games’ will be your Universe.

Step 2 : Let us further take the example of Games and let’s say we want to classify the games into indoor games and outdoor games. Make two small circles, intersecting each other, inside the Universe. Circle ‘A’ represents Outdoor games and circle ‘B’ represents Indoor games.

Step 3 : Now you have to fill in the circles according to the categories. This process of filling in is known as ‘populate’. Thus, fill in circle A with Football, Hockey and Cricket. Fill in circle B with Table Tennis and Chess.

Step 4 : Now you see, you are left with Basketball and Badminton because these are games that can be played both indoors and outdoors. Thus these two games fit in the intersection, or the overlap of the two circles A and B.

Step 5 : Now you are left with Video Games, which is a game but is very different from the indoor and outdoor games mentioned here. Thus, Video games will fall outside the two circles but inside the Universe.

Venn Diagram Facts

1. John Venn used the term ‘Eulerian Circles’ to name these diagrams.
2. Sometimes Venn diagrams can be represented by more than 3 sets, in the form of intersecting spheres.
3. Venn diagrams are not always made in circles but also in other different shapes.
4. Complex Venn diagrams are used in probability, computer science, statistics and logic.
5. If Circles do not intersect, then it is not a Venn diagram.

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