# Venn Diagram

Do you know what a Venn diagram looks like? Do you know who invented them?

We will learn all about them in this lesson.

Venn diagrams were invented by John Venn. He used them to show the similarities and differences between various sets visually. In this mini-lesson, we will explore the world of the Venn diagram by finding answers to the questions like what are Venn diagram symbols, Venn diagram application in math, and Venn diagram examples while discovering interesting facts around them.

## Lesson Plan

 1 What Is a Venn Diagram? 2 Challenging Questions on Venn Diagram 3 Important Notes on Venn Diagram 4 Solved Examples on Venn Diagram 5 Interactive Questions on Venn Diagram

## What Is a Venn Diagram?

A Venn diagram is a diagram that helps us visualize the logical 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 be used) to denote the relationship between sets.

Let us observe a Venn diagram example.

Here is the Venn diagram of the Universe. The correlation between the following set of numbers is easily understood using a Venn diagram. ### Subset

Let's look at another example.

There are two sets $$A$$ and $$B$$ in the figure below if $$A$$ and $$B$$ are two sets.

$$A$$ represents all the students in grade 5 while $$B$$ represents students of grade 5 who can swim.

If every element of set $$B$$ belongs to set $$A$$, then $$B$$ will be called a subset of $$A$$. This relationship is symbolically represented as $$\text A \subseteq \text B$$.

It is read as "$$B$$ is a subset of $$A$$" or "$$B$$ subset $$A$$."

Every set is a subset of itself. i.e. $$A \subseteq A$$.

Here is another example of subsets.

$$N$$ = set of natural numbers

$$I$$ = set of integers

Here N $$\subseteq$$ I, because all natural numbers are integers.

## What Are Venn Diagram Symbols?

There is a long list of about 30 Venn diagram symbols.

For an initial understanding, we shall stick to the below-given basic symbols.

1. The union symbol - $$\cup$$

2. The intersection symbol -  $$\cap$$

3. The complement symbol - $$A$$c or $$A$$' Let us now work on the data presented and learn the use of the symbols with this Venn diagram. Symbol It refers to Total elements (No. of students)

$$A$$ $$\cup$$ $$C$$

The number of students that prefer both burger or pizza and not a hotdog. 1 + 2 + 9 = 12
$$A$$ $$\cap$$ $$C$$ The number of students that prefer both burger and pizza and not a hotdog. 2
$$A$$ $$\cap$$ $$B$$ $$\cap$$ $$C$$ The number of students that prefer a burger, pizza as well as hotdog. 2
$$A$$c or $$A$$' The number of students that do not prefer a burger. 10 + 6 + 9 = 25

## How to Draw a Venn Diagram?

To draw a Venn diagram, first, the universal set should be known.

The universal set is usually represented by a rectangle.

Every set is the subset of the universal set ($$U$$).

Thus, every other set will be placed inside the rectangle.

The other subsets are represented by closed figures usually circles.

Universal set

Think of a bigger set that will accommodate all the given sets under consideration which in general is known as the Universal set.

Generally, the universal set is denoted by $$U$$, $$E$$, or $$\xi$$ and in the Venn diagram, it is represented by a rectangle. Examples

All the elements of set $$A$$ are inside the circle. Set $$A$$ is a subset of the universal set $$U$$.

They are part of the rectangle which makes them the elements of set $$U$$.

Thus, set $$A$$ will be represented as follows:

$$A$$ $$\cup$$ $$U$$ = $$U$$ From the above diagram, it is also clear that $$A$$ + $$A$$' = $$U$$

What will be the complement of a complement set? It will be set $$A$$ itself.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus