Venn Diagrams

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets . Venn diagrams are named after the English logician, John Venn (1834-1883).These diagrams consist of rectangles and closed curves usually circles. The universal set is represented usually by a rectangle and its subsets by circles.

Terms related to Venn Diagrams

Fig 1 - Universal Set

Universal Set

Whenever we use a set, it is easier to first consider a larger set called a universal set that contains all of the elements in all of the sets that are being considered.

Whenever we draw a Venn diagram:

• A large rectangle is used to represent the universal set and it is usually denoted by the symbol $U$.
• All the other sets are represented by circles or closed figures within this larger rectangle.
• Every set is the subset of the universal set $U$

Consider the Fig 1 . Here

• $U$ is the universal set with all the numbers $1-12$, enclosed within the rectangle.

• $A$ is the set of even numbers $2-12$, placed in a circle which is the subset of the universal set $U$ and it is placed inside the rectangle.
• All the numbers between $1-12$, that are not even, will be placed outside the circle and within the rectangle as shown above.
• $U=\{1,2,3,......,12\}$ is the universal set of which $A=\{2,4,6,8,10,12\}$is a subset.

Sub Set

Fig 2 - Sub Set

A subset is a set that is contained within another set. In the fig 2 we have two sets A and B. $A=\{2,4,6,8,10,12\}$ and $B=\{4,6,8\}$

Here, B is a subset of A which is represented by $B\subset A$. Circle B is contained within circle A. Also, all the elements of B are elements of set A . All these sets A and B are contained within the universal set $U=\{1,2,3,......,12\}$.