Venn Diagrams

Venn diagrams are useful in solving simple logical problems. Let us
study about them in detail. Mathematician John Venn introduced the
concept of representing the sets pictorially by means of closed
geometrical figures called Venn diagrams. In Venn diagrams, the
Universal Set ξ is represented by a rectangle and all other sets under
consideration by circles within the rectangle. In this chapter, we will
use Venn diagrams to illustrate various operations (union, intersection,
difference).

What are Venn Diagrams?

Pictorial representations of sets represented by closed figures are called set diagrams or Venn diagrams.

Venn diagrams are used to illustrate various operations like union, intersection and difference.

We can express the relationship among sets through this in a more significant way.

In this,

• A rectangle is used to represent a universal set.

• Circles or ovals are used to represent other subsets of the universal set.

Venn diagrams in different situations

• If a set A is a subset of set B, then the circle representing set A is drawn inside the circle representing set B.

• If set A and set B have some elements in common, then to represent them, we draw two circles which are overlapping.

• If set A and set B are disjoint, then they are represented by two non-intersecting circles.

In this diagrams, the universal set is represented by a rectangular
region and its subsets by circles inside the rectangle. We represented
disjoint set by disjoint circles and intersecting sets by intersecting
circles.