** Module: Venn diagrams**

- V00. Introduction
- V01. Basic notation
- V02. Everything and nothing
- V03. Exercises
- V04. Three circles
- V05. Exercises
- V06. Existence 1
- V07. Existence 2
- V08. Syllogism
- V09. Exercises
- V10. Limitations of Venn diagrams

** Quote of the page**

The great majority of men and women, in ordinary times, pass through life without ever contemplating or criticising, as a whole, either their own conditions or those of the world at large.

- Bertrand Russell

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So far we have been looking at Venn diagrams with two circles. We now turn to Venn diagrams with three circles. The interpretation of these diagrams is the same as before, with each circle representing a class of objects, and the overlapping area between the circles representing the class of objects that belong to all the classes.

As you can see from the diagram below, with three circles we can have eight different regions, the eighth being the region outside the circles. The top circle represents the class of As, whereas the circles on the left and the right below it represent the class of Bs and Cs respectively. The area outside all the circles represents those objects which are not members of any of these three classes.

You can click the different parts of the circles to see what they represent, and see if you understand why:

**The green region represents: **

Now that you know what each of the region represents, you should know how to use shading to represent situations where "Every X is Y", or "No X is Y". As before, shading an area indicates that nothing exists in the class that is represented by the shaded region.

Look at the sentences in the diagram below. Ask yourself which region should be shaded to represent the situation described by the sentence. Then click that sentence and check the answer.