https://file.aiquickdraw.com/mathbot/file/1729635745102j2af99wq.jpg

Let's work through the questions based on the Venn diagram provided:

### (a) Select all the genres that Ivanna likes.
Looking at the diagram, Ivanna is in the intersection of the three circles, meaning she likes **horror**, **nonsense**, and **romance**. So, the correct answers are:
- horror
- nonsense
- romance

### (b) How many students like horror or nonsense (or both)?
We need to count all the students in the regions associated with "Like horror," "Like nonsense," and their overlap. Here's the breakdown:
- **Horror** circle includes: Heather, Ryan, Karen, Ivanna, Alan, and Jim (6 students)
- **Nonsense** circle includes: Ryan, Karen, Tammy, Martina, Ivanna, Alan, and Austin (7 students)

However, Ivanna, Alan, Ryan, and Karen are in both circles, so we don’t want to double-count them. Using set union logic:

- Total number of students = 6 (horror) + 7 (nonsense) - 4 (overlap) = **9 students**

### (c) Which students only like one of the three genres (horror, nonsense, or romance)?
We need to identify students who are in only one of the circles. Based on the diagram:
- **Heather** is only in the horror circle.
- **Jim** is only in the horror circle.
- **Frank** is only in the romance circle.
- **Chris**, **Lisa**, and **Hans** are only in the romance circle.
- **Tammy** and **Martina** are only in the nonsense circle.

The students who like only one genre are:
- Heather
- Jim
- Frank
- Chris
- Lisa
- Hans
- Tammy
- Martina

Let me know if you want further clarification! Here are 5 follow-up questions based on this information:

1. How many students like all three genres?
2. Which students like both horror and romance but not nonsense?
3. How many students only like nonsense?
4. Which students like either romance or nonsense (or both)?
5. How many students dislike all three genres?

### Tip:
When working with Venn diagrams, remember to subtract the overlap when you're counting the total number of students in combined categories.

Based on the Venn diagram provided, answer the following questions:
(a) Select all the genres that Ivanna likes.
(b) How many students like horror or nonsense (or both)?
(c) Which students only like one of the three genres (horror, nonsense, or romance)? Choose all that apply.

Explore how to interpret a Venn diagram with multiple genres. This exercise involves set theory concepts such as unions, intersections, and exclusive sets. Suitable for students in Grades 6-8.

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