Venn Diagrams

A Venn diagram shows relationships between sets, using a rectangle for the universal set and circles for individual sets.

To see how this works, imagine a science department organizing sections for biology and chemistry labs. To manage resources and avoid scheduling conflicts, the department tracks student enrollment in the two courses.

Here, the rectangle represents all students in the department. Inside it, one circle represents Set A: students taking biology. Another circle represents Set B: students taking chemistry.

First, the department needs to know how many students are taking biology, chemistry, or both courses to plan resources. These students appear inside one or both circles. This is called A union B.

Next, the department needs to know which students are taking both courses to avoid scheduling conflicts. These students appear in the overlap of the circles. This is called A intersection B.

The nonoverlapping parts show students taking only biology or only chemistry. The space outside both circles shows students taking neither course.

So, using the Venn diagram, the department can count each group and plan lab resources more easily.