[V04] Three circles

Module: Venn diagrams

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Read not to contradict and confute; nor to believe and take for granted; nor to find talk and discourse; but to weigh and consider.

- Francis Bacon

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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:

§1. Shading

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.

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