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Based on the provided Venn diagram and instructions, let's break down the sets and solve the problems step by step.

We have:
- Set \( U \) represents all the animals in the shelter: 
  - \( U = \{ \text{rabbits, cats, turtles, fish, birds, dogs, gerbils, snakes, mice} \} \)
- Set \( P \) represents animals treated by Dr. Perry: 
  - \( P = \{ \text{rabbits, cats, turtles} \} \)
- Set \( R \) represents animals treated by Dr. Richardson: 
  - \( R = \{ \text{cats, turtles, fish, birds, dogs} \} \)

### (a) Set \( R' \) (the complement of set \( R \)):

This set will include all animals that are **not** in \( R \). 
- \( R = \{ \text{cats, turtles, fish, birds, dogs} \} \)
- So, \( R' \) includes the animals in \( U \) that are not in \( R \):
  - \( R' = \{ \text{rabbits, gerbils, snakes, mice} \} \)

- **Descriptive form**: "The set of animals that Dr. Richardson did not treat."
- **Roster form**: \( \{ \text{rabbits, gerbils, snakes, mice} \} \)

### (b) Set \( P \cap R' \) (the intersection of sets \( P \) and \( R' \)):

This set will include animals that are in both \( P \) and \( R' \). 
- \( P = \{ \text{rabbits, cats, turtles} \} \)
- \( R' = \{ \text{rabbits, gerbils, snakes, mice} \} \)

So, the common animals in both sets are:
- \( P \cap R' = \{ \text{rabbits} \} \)

- **Descriptive form**: "The set of animals treated by Dr. Perry but not by Dr. Richardson."
- **Roster form**: \( \{ \text{rabbits} \} \)

Would you like further details or clarification on any of these steps? 

Here are 5 related questions for further practice:
1. What is the union of \( P \) and \( R \)?
2. What is \( P' \), the complement of set \( P \)?
3. What is \( P \cup R' \)?
4. What is the intersection of \( P' \) and \( R \)?
5. How many animals are in both \( R \) and \( P \)?

**Tip**: When finding a complement of a set, always consider the universal set \( U \) and remove the elements in the original set.

A certain animal shelter has several animal types. We'll call the set of these animal types U. Two veterinarians treated certain animal types yesterday. Let P be the set of animal types treated by Dr. Perry. Let R be the set of animal types treated by Dr. Richardson. Use the Venn diagram to write the descriptive and roster forms of the sets below.

Learn how to solve a Venn diagram set theory problem involving two veterinarians treating animal types. This problem covers key concepts like set complement and intersection using Dr. Perry's and Dr. Richardson's treated animal sets. Suitable for Grades 6-9.

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