Venn diagrams: - Virtual University of Pakistan



Venn diagrams:

A diagram using circles to represent sets.

Actually shaded area represents the points inside a certain region.

One useful way of understanding the relations between sets is by using Venn diagrams. In a Venn diagram, sets are represented by points on a page. Points inside a certain region denote elements in a set.

For Example:-

Use a Venn diagram to represent the following:

1. A(B

2. A(B

3. A(Bc

4. B(Ac

Solution:-

1. A(B

[pic]

2. A(B

[pic]

3. A(Bc

[pic]

4. B(Ac

[pic]

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A Venn diagram is a pictorial representation of sets where sets are represented by enclosed areas in the plane.

The universal set U is represented by the interior of a rectangle, and the other sets are represented by circles lying within rectangle.

For Example:-

If A(B, then the circle representing A will be entirely within the circle representing B as in figure below:

[pic]

A(B

If A and B are disjoint, i-e., if they have no element in common, then the circle representing A will be separated from the circle representing B as in figure below:

[pic]

A and B are disjoint

However , if A and B are two arbitrary sets, it is possible that some objects are in A but not in B, some are in B but not in A, some are in both A and B, and some are neither A nor B; hence in general we represent A and B as in figure below:

[pic]

You can easily make Venn diagram in Paint. The procedure is that when you open paint document you can see the figures on the left hand side. Select the figure which you want to use in the Venn diagram.

Let’s suppose that first of all you want to make a rectangle. Then select rectangle from the figures and in the same way if you want to inset circle in the rectangle then select circle and paste in the rectangle. In this way you can make Venn diagram on paint document. Try it your self. You will understand more how to make Venn diagram in Paint.

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