Coupon Accepted Successfully!


Venn Diagrams

Most of the ideas about sets and their properties can be visualised by means of diagrams. These diagrams are known as Venn Diagrams. Venn Diagrams are named after the English logician John Venn(1834 - 1883).

John Venn(1834-1883)

In these diagrams, the universal set is usually represented by a rectangle and its subsets by circles, ellipses, square, triangle etc.

Whenever necessary, we specifically mark the elements of the set inside the diagram.

In visual below, the universal set U is given by
U = {a, b, c, d, e, f, g, h, i, j} and A = {b, c, f, g, j}.
In figure below the universal set U is given by

U = {a, b, c, d, e, f, g, h, i, j},
A = {b, f, j} and B = {c, g, j}.

Using a Venn diagram, the complement of a set can be visualised as the portion of the universal set that is outside A.

The complement of A is given by the shaded portion in the figure below:

Illustration 1
The idea that U is a universal set and A and B are two subsets of U with B A can be expressed by the Venn diagram.

Illustration 2
Let A = {x : x is a prime factor of 30}, B = {x : x is a prime factor of 42} and C = {x | x is a prime factor of 70}
Write the sets A, B and C in tabular form.
Also, represent the A, B and C using a Venn diagram.
We have A = {2, 3, 5}, B = {2, 3, 7} and C = {2, 5, 7}.

  1. Let U = {1, 2, 3, 4, 5} and A = {2, 3, 5}. Represent these sets by using Venn diagram.
  1. Represent the following sets by Venn diagram
    1. U = {a, b, c, d, e}, A = {a}
    2. U = {a, b, c, d, e}, A = {a, b}, B = {b, c} and C = {d, e}
  1. (a)
  1. Let U be the universal set. Represents two subsets A and B of U using Venn diagram where A and B are such that A and B have no elements in common.



Test Your Skills Now!
Take a Quiz now
Reviewer Name