Venn diagram

A Venn diagram is a pictorial representation of the relationships between sets. Venn diagrams were invented by a man named John Venn as a way of picturing relationships between different groups of things.

The invention of this forms of diagram it seems was pretty much all he ever accomplished. However, much of what we know today as "Venn diagrams" are in point of fact "Euler" diagrams.

Nevertheless we will continue to use the usual "Venn" terminology for the purposes of this lesson. In view of the fact that the mathematical term for "a group of things" is "a set", Venn diagrams can be used to illustrate both set relationships and logical relationships.

To draw a Venn diagram, you first draw a rectangle which is called your "universe". In the context of Venn diagrams, the universe is not "everything", but "everything you're dealing with right now". For example, we can deal with the following list of things: moles, swans, rabid skunks, geese, worms, horses, Edmontosorum (a lot of duck-billed dinosaurs), platypusses, and a very fat cat.

Use of Venn diagram to represent set operations

We use diagrams or picture in geometry to explain a concept of a situation. Occasional we as well make use of them in problem solving.

In mathematics, we make use of diagrammatic representations known as venn diagrams see the relationships between sets and set operations

We can represent sets using Venn diagrams. In a Venn diagram, the sets are represented by shapes; usually circles or ovals. The elements of a set are labelled within the circle.

Drawing and Shading Venn Diagrams

Sometimes you may be given the description of a few sets and you are asked to draw a Venn diagram to demonstrate the sets. A Venn Diagram is a pictorial representation of the relationships between sets. In this section, we will learn how to shade required regions of a Venn Diagram. We will learn how to shade regions of two sets and three sets.

First, we require to: find out the relationships between the sets like subsets and intersections. There may be a lot of ways to describe the relationships.

We then draw A inside B if we know that:

All members of set A belongs to set B or A ⊂ B or A ∪ B = B or A ∩ B = A

Or n (A ∩ B) = n (A)

Secondary, we would draw A and extend it beyond B if we know that:

A few members of A belongs to B or A ∩ B ≠ Ø or n (A ∩ B ) ≠ 0

Next, we would draw disjoint sets A and B if we know that

no elements of A belongs to B or A ∩ B = Ø or n(A ∩ B ) = 0

Example:

U = the set of triangles, I = the set of isosceles triangles,

Q = the set of equilateral triangles and R = the set of right-angled triangles.

Draw a Venn diagram to illustrate these sets.

Solution:

First, we determine the relationships between the sets.

All equilateral triangles are isosceles, so Q ⊂ I. (within)

A few right-angled triangles may be isosceles. R ∩ I ≠ Ø (overlap)

Right-angled triangles can never be equilateral. R ∩ Q = Ø (disjoint)

Then we draw the Venn diagram:

Example:

Given the set P is the set of even numbers between 15 and 25. Draw and label a Venn diagram to represent the set P and indicate all the elements of set P in the Venn diagram.

Solution:

List out the elements of P.

P = {16, 18, 20, 22, 24} ← ‘between’ does not include 15 and 25

Draw a circle or oval. Label it P. Put the elements in P.

The universal set

Often times it is essential to consider a set that embodies all elements related to a particular discussion. Such set that contains all the elements under consideration in a Particular discussion is referred to as universal set and it is denoted by U. The universal set may differ from question to question.

For instance:

If the elements presently under discussion are integers, then the universal set U is the set of all integers and is represented as follows:

In a Venn diagram, the universal set is usually represented by a rectangle and its proper subsets are represented by circles or ovals inside the rectangle. We write the names of its element inside the figure.

Complement of a set

The set of all elements of U (universal set) that are not elements of the subsets are referred to as complement of the set. The complement of a set A is represented by A’ read as A PRIME

Union of two sets

The union of two sets A and B is the set of the elements which are in A or B or in both A and B. It is written as A U B.

Intersection of Sets

The intersection of two sets A and B is the set of all elements common to both A and B. It is denoted as A ∩ B, it is read as A intersection B

Representation of set operations with the use of Venn diagram

We have presented below a few more set operations in Venn diagram: View more on psalmfresh.blogspot.com for more educating and tricks article Thank you