https://file.aiquickdraw.com/mathbot/file/172542224400722qw6vet.jpg

Let's analyze the problem provided in the image and solve it step by step.

### Problem Analysis:
We have the following information about a class of 20 students:
- 8 students are wearing a t-shirt but not shorts.
- 12 students are wearing a t-shirt (this includes students wearing only a t-shirt and those wearing both a t-shirt and shorts).
- 5 students are wearing neither a t-shirt nor shorts.

### Step 1: Draw the Venn Diagram
We need to consider two sets:
- Set A: Students wearing t-shirts.
- Set B: Students wearing shorts.

### Step 2: Fill in the Given Information
- The total number of students is 20.
- The number of students in Set A (wearing t-shirts) is 12.
- The number of students wearing only a t-shirt (and not shorts) is 8.
- The number of students in neither set (neither t-shirt nor shorts) is 5.

#### Step 3: Solve for Overlapping and Remaining Values
Let:
- \( x \) be the number of students wearing both a t-shirt and shorts.
  
Then:
- Students wearing only a t-shirt = \( 12 - x = 8 \) (from the information given)
  
  So, \( x = 4 \) (students wearing both a t-shirt and shorts).
  
- Total students wearing shorts, Set B = \( x + \) (students wearing only shorts) = \( 4 + y \).
  
  To find \( y \) (students wearing only shorts), we can use the total number of students:
  - Students wearing neither = 5
  - Thus, \( 20 - (8 + 4 + y) = 5 \)
  - Simplifying: \( 12 + y = 15 \), so \( y = 3 \).

#### Step 4: Answer the Final Question
Now, we know that:
- Students wearing only shorts: 3
- Students wearing both t-shirts and shorts: 4

So, the total number of students wearing shorts is \( 3 + 4 = 7 \).

### Final Answer:
**7 students were wearing shorts.**

Would you like further details or have any questions?

### Related Questions:
1. What is the significance of a Venn diagram in solving set-related problems?
2. How would the problem change if the number of students wearing neither a t-shirt nor shorts was different?
3. How can we apply the principles of Venn diagrams to more complex problems involving three or more sets?
4. What other methods besides Venn diagrams can be used to solve this type of problem?
5. Can you explain the importance of intersection and union in set theory with an example?

### Tip:
When solving problems involving sets, always ensure that you account for every possible group (e.g., only in set A, only in set B, both in A and B, neither in A nor B) to avoid missing any data.

In this hot weather, a class of 20 students has:
- 8 students who are wearing a t-shirt but not shorts,
- 12 wearing a t-shirt,
- 5 that are wearing neither a t-shirt nor shorts.

Draw a Venn diagram to show the above information, then solve the diagram.
Finally, answer the question "How many of the students were wearing shorts?"

Explore how to solve a set theory problem using a Venn diagram. Given a class of 20 students, determine how many were wearing shorts by analyzing data such as the number wearing t-shirts only, both, or neither. This problem is ideal for students in Grades 6-8 and focuses on key concepts like Venn diagrams and logical reasoning.

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