# 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)**

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

In visual below, the universal set U is given by

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 âŠ‚ 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.

**Example**

**Let U = {1, 2, 3, 4, 5} and A = {2, 3, 5}. Represent these****sets by using Venn diagram.**

**Solution**

- Represent the following sets by Venn diagram
- U = {a, b, c, d, e}, A = {a}
- U = {a, b, c, d, e}, A = {a, b}, B = {b, c} and C = {d, e}

**Solution**

- (a)

(b)

**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.**

**Solution**