# Venn Diagrams

Venn diagram is a diagrammatical representation of sets. A Venn diagram consists
of a rectangle where the universal set U, is represented by interior of the rectangle.
The other sets are represented by circles or ellipses. The elements or members of
a set are written inside the circle.

**For example:**

The Venn diagram of AJ B (A is subset
of B) will be drawn as:

If A and B are two mutually exclusive or disjoint sets then the Venn diagram will be:

Below are a few more examples of Venn diagrams:

If A and B are two mutually exclusive or disjoint sets then the Venn diagram will be:

Below are a few more examples of Venn diagrams:

- An example of a Venn diagram to represent set operations (union, intersection and
compliment) is given below:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {3, 4, 5, 7} and B = {1, 2, 4, 7}

Then A T B = {1, 2, 3, 4, 5, 7} and A B = {4, 7} and A' = U – A = {1, 2, 6, 8, 9, 10}

Hence Venn diagram of the above example will be:

- Given a set I = {x: 3x – 2 < 13, x is a positive integer}. Then draw a Venn diagram
to represent the set I.

**Solution:**

First we have to solve the value of x from the given equation,

3x – 2 < 13

L 3x < 15

L x < 5

Hence I = {1, 2, 3, 4}, so the Venn diagram will be:

- Draw a Venn diagram of A – (B S C).

**Solution:**

The shaded portion represents A – (B S C)

- Draw a Venn diagram of A T (B – C).

**Solution:**

First we will draw B – C which is:

B - C

Now the intersection of A and (B – C) will be:

A T (B – C)

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