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.

Now move the cursor over the numbered regions of the diagram to see what they represent :

V02.1 Shading

So look at the sentences in the diagram below. Ask yourself which area you should shade to represent the situation described by the sentence. Then move the cursor over that sentence and the answer will be displayed.

Notice that the diagram shows that there are three pairs of sentences which are logically equivalent, in that each pair describe exactly the same situation and so they must always have the same truth-value. Which ones are they?

V02.2 Exercises

Q1 Is the statement "Every C is a B" true according to this diagram? [Show answer] Correct.

Q2 Is the statement "No A is a B" true according to this diagram? [Show answer] No. Since the overlapping area between circles A and B has not been shaded, the diagram does not rule out the possibility that some A is a B.

Q3 Is the diagram consistent with the statement "Something is A"? [Show answer] Yes. There is still one unshaded region within the A cricle.

Q4 "If something is A it is either B or C." Is this statement true according to this diagram? [Show answer] No. The regions where A overlap with B or C are all shaded.

Q5 Is the diagram consistent with the statement "Something is A"? [Show answer] Yes. The A circle still has an unshaded region.

Q6 "Something is A if and only if it is not C." Is this statement true according to this diagram? [Show answer] Yes. The only unshaded A region does not overlap with the only unshaded C region.

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