    # 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:

• 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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Other topics under Set Theory:       • 