Sets-Venn Diagrams

Let’s understand what the Venn diagram is!

A Venn diagram is a graphic that employs circles to depict relationships between objects or finite groups of objects. Circles that overlap share characteristics, whereas circles that do not overlap do not.

Venn diagrams visually depict the similarities and differences between two concepts. They’ve long been acknowledged as valuable instructional resources. Venn diagrams have been utilised as a part of the introductory logic curriculum and in elementary-level educational plans worldwide since the mid-20th century.

Venn diagram history

John Venn, a British logician, is the name given to Venn diagrams. In 1880, he published a paper in the Philosophical Magazine and Journal of Science titled “On the Diagrammatic and Mechanical Representation of Propositions and Reasonings.”

However, the origins of this figure style can be traced back at least 600 years. In a 1969 article tracing their history, author M.E. Baron said that philosopher and logician Ramon Llull (often written Lull) of Majorca employed a similar diagram style in the 1200s. According to her, similar designs were also drawn by German mathematician and Gottfried Wilhelm von Leibnitz, philosopher in the late 1600s.

Venn diagram purpose and benefits

• To graphically organise information so that commonalities and contrasts between sets of objects can be seen. They can be used by students and professionals to work through the logic of an idea and to visualise the relationships for visual communication. This might be anything from a simple to a complex goal.
• To contrast two or more options and evaluate what they have in common against what might set them apart. This could be done while choosing a significant-good or service to purchase.
• To be able to answer complex mathematical problems. Of course, this assumes you’re a mathematician.
• To analyse data sets, detect relationships, and forecast the likelihood of specific events.
• To deduce the reasoning behind statements or equations, such as the Boolean logic underlying a word search with “or” and “and” statements and how they’re arranged.

Venn Diagram for Sets Operations

We can execute certain operations on given sets in set theory. The following are the operations:

Union of Sets Venn Diagram

A ∪ B = {x | x ∈ A or x ∈ B} can be used to express the union of two sets, A and B. A Venn diagram with two circles can be used to describe this operation on the items of sets A and B. The union of sets A and B is the combined region of both circles.

The intersection of Set Venn Diagram

A ∩ B = {x: x ∈ A and x ∈ B} is the intersection of the two sets A and B. A Venn diagram with two overlapping circles can be used to describe this process on sets A and B. The intersection of Set A and Set B is indicated by the region that is shared by both circles.

Complement of Set Venn Diagram

A’ can be used to represent the complement of any collection A. This symbolises items that aren’t in set A and can be represented with a circle in a Venn diagram. A’s complement is the region covered by the universal set, excluding the region covered by set A.

Difference of Set Venn Diagram

The difference between the two sets can be expressed as A – B. It’s also known as a “relative complement.” A Venn diagram with two circles can be used to represent this set operation. The difference between sets A and B is the area covered by set A minus the area shared by both sets A and B.

How to Draw a Venn Diagram?

After understanding what the Venn diagram is, let’s understand how to simply draw it! There are no limits to how many circles can be created in a Venn diagram. We normally only include two or three circles in a Venn diagram because more than three becomes exceedingly difficult. The following are the four simple stages of drawing a Venn diagram:

Step 1: Sort all of the things into groups.

Step 2: Draw a rectangle and label it according to the sets’ association.

Step 3: Draw the circles in the appropriate amount of categories.

Step 4: Arrange the pieces in the appropriate circles.

Applications of Venn Diagram

Using Venn diagrams has many advantages. A Venn diagram is used to illustrate concepts and groups in various domains, such as statistics, linguistics, logic, education, computer science, and business.

• We can visually organise data to see the relationships between elements, such as commonalities and differences, and portray those relationships for visual communication.
• We can compare two or more subjects and see what they have in common and what they have in common. This could be done while choosing significant goods or services to purchase.
• Mathematicians often use Venn diagrams to solve difficult equations.
• Venn diagrams can be used to compare data sets and uncover correlations.
• You can utilise Venn diagrams to deduce the reasoning behind statements or calculations.

Conclusion

A Venn diagram can be defined as the diagram that aids in visualising the logical association amid sets and their elements and the solution of cases grounded on these sets. A Venn diagram commonly utilises intersecting and non-intersecting circles (although other closed shapes such as squares may be used).