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Venn Diagrams (page 1 of 4) Sections: Introduction, Logic and set notation, Setnotation exercises, Venn word problems Venn diagrams were invented by a guy named John Venn (no kidding; that was really his name) as a way of picturing relationships between different groups of things. (Inventing this type of diagram was, apparently, pretty much all he ever accomplished. To add insult to injury, much of what we refer to as "Venn diagrams" are actually "Euler" diagrams. But we'll stick with the usual "Venn" terminology for the purposes of this lesson.) Since the mathematical term for "a group of things" is "a set", Venn diagrams can be used to illustrate both set relationships and logical relationships. To draw a Venn diagram, you first draw a rectangle which is called your "universe". In the context of Venn diagrams, the universe is not "everything", but "everything you're dealing with right now". Let's deal with the following list of things: moles, swans, rabid skunks, geese, worms, horses, Edmontosorum (a variety of duckbilled dinosaurs), platypusses, and a very fat cat.
The overlap of the two circles, containing only "platypusses", is called the "intersection" of the two sets. (By the way, the plural of "platypus" is not "platypi", but is, in general [Australian] usage, "platypusses", though I have learned that the technicallycorrect plural is apparently "platypode".) When drawing Venn diagrams, you will probably always be dealing with two or three overlapping circles, since having only one circle would be boring, and having four or more circles quickly becomes astonishingly complicated. Venn diagrams have two general applications: explaining set notation, and doing a certain class of word problems. We'll look at set notation first.... Top  1  2  3  4  Return to Index Next >>



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