It's a funny old world. If you'd asked me this morning if I understood Venn diagrams, my answer would have been a resounding" "Yes!" Quite apart from anything else, some time ago I penned a rather interesting paper on the history of Logic Diagrams and Machines, which ranged from the Tree of Porphyry, to John Venn and his diagrams, to Benjamin Burack and his logic machine.
Also, I did a quick search on the web, and found a Really Useful Website that covers a lot of ground with regards to Venn diagram. This didn't really tell me anything I didn't already know, but it has some cool diagrams and showed me things in a way I hadn't seen them presented before.
There's just one problem. I have a niggling recollection that I saw something about Venn diagrams a long time ago, and I can't quite remember what it was. So I'm asking for your help. Consider the diagram below. At the top we have a classic Venn representation. The rectangle is the "universe" containing everything. The two overlapping circles represent two "classes" called A and B. The area where the two circles intersect equals A AND B; the total area covered by both circles equals A OR B; and the area outside the two circles equals NOT(A) AND NOT(B), which – using a standard DeMorgan Transformation is the same as saying NOT(A OR B).
Now look at the shaded area in the middle diagram; this equals A AND NOT(B). No problems thus far. But what about the bottom diagram with the cross-hatched lines? This where I am having a problem, because I vaguely remember seeing something about this ages and ages ago. As I recall, the use of cross-hatched lines means that this area represents something different to the shaded area in the middle diagram. Does anyone know anything about this? Is it just my imagination, or does this actually mean something?
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