ABSTRACT
First some general questions:
Does an unshaded diagram make a statement? If so, what do these diagrams state?
https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig275_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>Does a shaded diagram make a statement? If so, what do these diagrams state?
https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig276_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>3 What about these?
https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig277_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig278_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>Does the frame below mean the diagram states that geese, hens and anything that swims are all birds? If not, what is it doing?
https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig279_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> I can use shading to make any statement that says a set represented in my diagram is empty. These can be quite complicated. For example I can say, 'All Swiss people speak either French or German or both': https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203061350/f5ce7580-7c0c-4392-aeab-0c1bd683fe20/content/fig280_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> and I can also say, 'all Swiss people speak either French or German, but not both'.How would I say that, using three circles?
Now say each of them again, using two circles and a frame instead.
