# 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.

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets