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Complete Information about Venn diagrams

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In mathematics, we are performing several operations including addition, subtraction, division, and multiplications. We use two elements to do these operations. Then, the result we get after performing the mathematical function is the solution for us.

The diagram representing the sets and the relation between them and the operations performed on these sets are the Venn diagrams. These sets have been prepared using the pictorial way. John Venn (1894-1883) had introduced the Venn diagrams concept.

He had made some circles and then prepared a concept showing the relationships in those sets. On the other hand, it is a vital concept in geometry. We often call the Venn diagram the logic diagram or set diagram.

Furthermore, these diagrams show the operations on the sets like union and intersection. On the other hand, diagrams are helpful in depicting the subsets of a particular set.

Fox Example: The subsets of natural numbers are whole numbers. Furthermore: The Whole numbers have been referred to as the subset of integers. Using the Venn diagram, we can show that whole numbers, natural numbers, and integers are universal sets.

Definition of Venn diagram

The diagram form representation to show relation between two sets is Venn diagram. We are using the circles and drawing them to represent the Venn diagrams. On the other hand, we want to represent the universal set then; we use the rectangle shape.

Using these geometry representations, we can show the relation between two sets X and Y with the universal set by drawing a useful diagram. Example: Set X: odd numbers, Y: even numbers, and the universal set contain all the natural numbers. The formula that we are using it to solve the above problem is n(X ⋃ Y) = n(X) + n(Y) – n(X ⋂ Y).

Formula to solve the three-set Venn diagrams

Therefore, the formula that we use in the geometry for solving the three-set Venn diagram is:

n(A ⋃ B ⋃ C) = n(A) + n(B) + n(C) – n(A ⋂ B) – n(BC) – n(A-C) + n(A ⋂ BC)

On the other hand, the symbols that have used in the representation of the sets are:

  • ∪: Union between the sets
  • ∩: Intersection
  • A’ or Ac: Symbol that shows the complement of a particular set

Guide to draw a proper Venn diagram to understand the concept

You want to draw the Venn diagram. Collect the information about the two sets and the universal set. Every set we have in the diagram is the subset of the universal set. Therefore, we use the rectangle diagram to represent the universal set, and on the other hand, the circle shape is used for drawing the sets. The sets are the subsets of the universal set in the Venn diagram.

Set of Operations in Venn diagram

According to the set theory, the list of the diagrams that we perform using the Venn diagram is as follows:

Union

The symbolic description to describe the union between the two sets A and B as A ∪ B = {a: a ∈ A or a ∈ B}.

Intersection

The common part between sets A and B is the intersection with these two sets.

Complement

(A ∪ B)’ it represents, as the complement of set A is the union of set B. Additionally; it shows that no elements of Set A and B are part of the universal set.

Difference

A-B shows the difference between A and B. On the other hand, we refer to it as the relative complement too sometimes. We will show the elements that are not part of set A and B using the difference operation concept. Book a class at Cuemath to understand the concepts.

Conclusion

We have discussed the set theory and the operations applied to it in the article. Sets and geometry are essential concepts in mathematics. You are beginning to do the functions related to sets before collecting the information about the universal set and two sets.

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