As a new subscriber, I have folled with some interest (and in some cases, amusement) several ongoing discussions on several topics the past weeks. Now I can't resist putting my oar in the water concerning the discussion on Venn Diagrams.
The original problem as stated about the residents of New Mexico and Albuquerque was couched in terms of what are usually known as Euler's Circles which do not include all logical possibilities. Venn was interested in getting the logical possibilites covered. He would have taken issue with some of the statements in many commonly used texts of today.
Finally, Ms. Addington's response about the blobs with fingers (which is a possible way of doing it with 4 subsets) prompted me to enter this discussion. A Venn diagram is supposed to be a visual aid. Four circles cannot be made to show the universe partitioned into 16 subsets, but 4 congruent ellipses can be intersected nicely to do this. Five subsets can be shown with 32 partitions by superimposing a circle with a hole in it on the 4 ellipses. I refer you to an article in the February 1963 MATHEMATICS TEACHER by Sister M. Stephanie, entitled "Venn Diagrams", pp.98-101. I hope this adds clarification, not confusion to the discussion.
John E. Young - a classroom teacher from grades 7 - 12 for 9 years and now in Teacher Training. John E. Young Professor of Mathematics Southeast Missouri State University Cape Girardeau, Missouri, 63701 (314) 651-2771