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The question involves organizing students into groups based on two different project types: **graphing (G)** and **writing a paper (P)**. Additionally, each student works on one of four subject areas: **economics (E)**, **finance (F)**, **sociology (S)**, or **criminal justice (C)**. The Venn diagram has two circles:

- **Circle A**: Represents students working on a graphing project.
- **Circle B**: Represents students working on a paper.

### Dot Labels:
- **GF**: Graphing project in finance.
- **GE**: Graphing project in economics.
- **GS**: Graphing project in sociology.
- **GC**: Graphing project in criminal justice.
- **PF**: Paper project in finance.
- **PE**: Paper project in economics.
- **PS**: Paper project in sociology.
- **PC**: Paper project in criminal justice.

### Steps for Sorting the Dots:
1. **A (Graphing Project)**: Dots corresponding to students working on graphing projects should be placed in **Circle A**.
   - **GF, GE, GS, GC** will be outside Circle B because these students are working only on graphing projects.

2. **B (Paper)**: Dots corresponding to students working on papers should be placed in **Circle B**.
   - **PF, PE, PS, PC** will go inside **Circle B**, but not in **Circle A**, since they are exclusively working on papers.

### Intersection of A and B (A AND B):
- Since each student is working on either a graphing project or a paper, there are no students working on both. Thus, the intersection (middle area) should remain empty.

### Final Placement:
- **Circle A** (Graphing project): Place **GF, GE, GS, GC** outside the overlap.
- **Circle B** (Paper): Place **PF, PE, PS, PC** outside the overlap.

Let me know if you need further clarification or have additional questions! 

### Related Questions:
1. What happens if a student is allowed to work on both a graphing project and a paper?
2. How can we extend this problem if there are more subject areas?
3. How would the Venn diagram change if some students were not assigned to any project?
4. What if students could choose between multiple subjects, requiring multi-category organization?
5. How could this problem be solved with probability theory?

### Tip:
When using Venn diagrams, always check if the sets overlap, and make sure to carefully sort the labels into distinct, shared, or exclusive areas.

A mathematics professor is organizing her classroom into groups for the final project. Each student will either be working on a graphing (G) project or writing a paper (P). Also, each student will be working on an economics (E), finance (F), sociology (S), or criminal justice (C) problem. The dots in the Venn diagram show the different scenarios. Let A be the event of a student working on a graphing project. Let B be the event of a student writing a paper. Move the dots on the Venn diagram to place them in the correct event A, B, or A AND B.

A detailed solution for a classroom organization problem involving graphing projects and paper writing using Venn diagrams. Learn how to classify students based on subjects such as economics, finance, sociology, and criminal justice. This problem covers key concepts in set theory and Venn diagrams, suitable for students in grades 9-12.

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