Venn Diagrams

Venn Diagrams are a way to show in picture form how sets relate to each other. You can represent the Union and Intersection discussed in the previous page within the Venn Diagrams. The easiest way is to show an example:

The sets used in these examples will be:




So if you remember the section on union and intersection the following would also be true:

A intersect B = {6,8}

A intersect C = {4,5,8}

So if we take the intersect of them all we get:

A intersect B intersect C = {8}

This is because 8 is the only element in all 3 sets.

Now back to venn diagrams. If we wanted to represents these 3 sets and how they interact with each other we would have the following Venn Diagram:

As you can see the diagram helps you visualize how the sets intersect each other. Each of the circles represents one of the sets. Where the circles overlap are the intercept of the sets. Since 8 is the only element in all three circles it is the only one in the middle.

Practice Question

In the above venn diagram shade in the part of the diagram that represents:

A intersect B

B intersect (A union C)

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