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Topic: More on Venn Diagrams
Replies: 0

 Dr. John Young Posts: 1 Registered: 12/6/04
More on Venn Diagrams
Posted: Dec 11, 1995 11:34 AM

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.

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