Drawing Venn You Feel Like It in VS .NET

Encoder QR Code in VS .NET Drawing Venn You Feel Like It

Venn diagrams are pictures that show the relationships between two or more sets and the elements in those sets The adage a picture is worth a thousand words is never truer than with these diagrams Venn diagrams can help you sort out a situation and come to a conclusion Many problems that you solve by using Venn diagrams come in paragraphs plenty of words and numbers and confusing relationships Labeling the circles in the diagrams and filling in numbers helps you determine how everything works together and allows you to see if you ve forgotten anything You usually draw Venn diagrams with intersecting circles You label the circles with the names of the sets, and you encase the circles with the universal set (a rectangle around the circles) The elements shared by the sets are shared by the overlapping parts of the respective circles For instance, the Venn diagram in Figure 17-1 shows set A, which contains the letters of the alphabet that spell encyclopedia, and set B, which contains the letters in the alphabet that rhyme with see Both sets are encased in the universal set all the letters in the alphabet

Notice that the letters c, d, e, and p appear in both sets The Venn diagram makes it easy to see where the elements are and what characteristics they have

The business of sorting letters based on their placement in a word or what they rhyme with, which you see in examples in the previous section, may not seem very fulfilling The actual applications get a little more complicated, but the examples here show you the basics Some actual uses of Venn diagrams appear in the world of advertising (charting types of advertising and the results), of politics (figuring out who has what opinions on issues and how to make use of their votes), of genetics and medicine (looking at characteristics and reactions based on symptoms and results), and so on The following example shows, in a simplified version, how useful Venn diagrams can be A Chicago-area newspaper interviewed 40 people to determine if they were Chicago White Sox fans and/or if they cheered for the Chicago Bears (For those of you who could care less about sports, the White Sox are a baseball team, and the Bears are a football team) Of the people interviewed, 25 are White Sox fans, 9 like both the Sox and the Bears, and 7 don t care for either team How many people are Bears fans As you can see, 25 + 9 + 7 = 41, which is more than the 40 people interviewed The process has to have some overlap You can sort out the overlap with a Venn diagram You create one circle for White Sox fans, another for Bears fans, and a rectangle for all the people interviewed Start by putting the seven fans who don t cheer for either team outside the circles (but inside the rectangle) You then put the nine who like both teams in the intersection of the two circles (see Figure 17-2)

The number of White Sox fans is 25, so, if you put 16 in only the Sox s circle, the number in the entire circle (including the overlap) sums to 25 The only area missing is the circle where people are Bears fans but not Sox fans So far, you have a total of 25 + 7 = 32 people Therefore, you can say that 8 people root for the Bears but not the Sox You put an 8 in that area, and you see that the number of Bears fans totals 17 people (see Figure 17-3)