In your homework you've been working with Venn Diagrams. These provide a nice way of visualizing groupings of data when you're splitting outcomes into only 2 or 3 categories. The reason this is restricted to no more than 3 groupings is that with 4 or more categories, there's not a simple 2-dimensional way to visualize all the possible overlappings. For instance, in a Venn Diagram with 3 sets, there are 8 different regions shown in your picture. (One of the 8 regions in the picture is the white region outside all the circles.) But if you had 4 sets instead of 3, there would be 16 regions, and there's no obvious way to draw 4 circles and display all the 16 sub regions.
So the main use of Venn Diagrams is to visualize simple examples as a way of getting your brain working well enough to understand more complex groupings of data. From a theoretical standpoint, it's what comes next that is more important. But Venn Diagrams provide a useful introduction that sets the stage for the multiplication principle, combinations, and permutations which are the topics on the horizon.
Friday, February 19, 2016
