Venn Diagram

A graphical representation of the various ways in which different sets may be related to one another. Any closed figure, such as a circle or a polygon, can serve as an accurate representation of a Venn diagram (square, hexagon, etc.). In most cases, though, we will use circles to depict each group.

A Venn diagram is depicted as a rectangular shape surrounding the universal set in the preceding figure. This universal set contains two separate sets, which are denoted by the letters X and Y. As a result, X and Y are not part of the same set. A circle serves as a representation for the two sets that are being discussed here, X and Y. This figure illustrates that sets X and Y are not connected to one another in any way, but that they are both components of a larger, more general set.

Set X, for instance, can be interpreted as “Set of even numbers,” whereas Set Y can be interpreted as “Set of odd numbers,” and Universal Set U can be interpreted as “Set of Natural Numbers.”

We can use the below formula to solve the problems based on two sets.

n(X ⋃ Y) = n(X) + n(Y) – n(X ⋂ Y)

Representation of Sets in a Venn Diagram

A Venn Diagram Showing the Representation of the Sets

It is carried out in accordance with the following:

A Venn Diagram Showing the Representation of the Sets

It is carried out in accordance with the following:

• The majority of each individual set’s representation is that of a circle, and the circle is contained within a square (the quadrilateral represents the finiteness of the Venn diagram as well as the Universal set.)

• Labeling is done for each set with the set’s name to indicate the distinction, and the circles have the various elements that make up each set inscribed within them.

• Sets that share no elements are shown individually, while sets that share some elements are shown overlapping one another. Sets that share no elements are shown separately from sets that share some elements.

• The elements are written within the circle that represents the set that contains them, and the elements that are common to both sets are written in the areas of the circles that overlap.

Venn Diagram Formula

The formula for a Venn diagram is used to identify one of the following for any two sets A and B that are supplied: the number of elements of A, the number of elements of B, the number of elements of A U B, or the number of elements of A ⋂ B when the other three are given. According to the formula:

● n (A U B) = n(A) + n(B) – n (A ⋂ B)

In this context, the numbers n(A) and n(B) stand for the total number of elements found in arrays A and B, respectively. The number of elements in set A U B is denoted by the notation n(A U B), while the number of elements in set A B is denoted by n(A ⋂ B). The following is what the formula looks like when it is extended to cover three sets:

● n (A U B U C) = n(A) + n(B) + n(C) – n(A ⋂ B) – n(B⋂C) – n(C ⋂ A) + n(A ⋂ B ⋂ C)

Conclusion 

These diagrams are also known as Set Diagrams or logic Diagrams, and they display the various Sets of operations that may be performed on a set, such as the intersection of the set, the union of the set, and the difference of sets. A Set can also be represented by its SubSets using this notation.

The set of natural numbers, for instance, is a subset of the set of whole numbers, which in turn is a subset of the set of integers. The Venn diagram is a useful tool for illustrating the relationship that exists between the sets of natural numbers, whole numbers, and integers. The set of integers is considered to be the universal set. Check out the diagram below here.

The letters W stand for whole numbers, while the letters N stand for natural numbers.