Practice for students Grade 9 - SETS Theory Interactive Worksheet ... - Free Printable

Let's solve the problems step by step using the Venn diagrams provided.

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Problem 1: Venn Diagram for Consoles (XBox, PS3, Wii)

#### Venn Diagram:
- XBox: 7 (only XBox), 5 (XBox and PS3), 9 (XBox and Wii)
- PS3: 3 (only PS3), 5 (PS3 and XBox), 2 (PS3 and Wii)
- Wii: 2 (only Wii), 9 (Wii and XBox), 2 (Wii and PS3)

#### Questions:

1. How many students owned an Xbox?
- Students who own an Xbox are in the entire XBox circle.
- This includes:
- Only XBox: 7
- XBox and PS3: 5
- XBox and Wii: 9
- Total: \( 7 + 5 + 9 = 21 \)

2. How many students owned an Xbox and a PS3?
- This is the intersection of the XBox and PS3 circles.
- Value: 5

3. How many students owned at least two consoles?
- Students who own at least two consoles are in the intersections of the circles.
- These are:
- XBox and PS3: 5
- XBox and Wii: 9
- PS3 and Wii: 2
- Total: \( 5 + 9 + 2 = 16 \)

4. How many students owned an Xbox or a Wii?
- Students who own an Xbox or a Wii are in either the XBox circle or the Wii circle.
- This includes:
- Only XBox: 7
- XBox and PS3: 5
- XBox and Wii: 9
- Only Wii: 2
- Wii and PS3: 2
- Total: \( 7 + 5 + 9 + 2 + 2 = 25 \)

5. How many students owned an Xbox and PS3, but not a Wii?
- This is the intersection of XBox and PS3, excluding those who also own a Wii.
- Value: 5 (since no one in the XBox and PS3 intersection also owns a Wii)

6. How many students owned no console?
- The total number of students surveyed is 40.
- Students who own at least one console are in the union of all three circles.
- Total students owning at least one console:
- Only XBox: 7
- Only PS3: 3
- Only Wii: 2
- XBox and PS3: 5
- XBox and Wii: 9
- PS3 and Wii: 2
- Total: \( 7 + 3 + 2 + 5 + 9 + 2 = 28 \)
- Students with no console: \( 40 - 28 = 12 \)

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Problem 2: Venn Diagram for Pizzas (Mushrooms, Cheese)

#### Venn Diagram:
- Mushrooms: 5 (only Mushrooms), 8 (Mushrooms and Cheese)
- Cheese: 12 (only Cheese), 8 (Mushrooms and Cheese)
- Outside both: 8 (no toppings)

#### Questions:

7. How many people ordered pizzas with Mushrooms?
- People who ordered pizzas with Mushrooms are in the entire Mushrooms circle.
- This includes:
- Only Mushrooms: 5
- Mushrooms and Cheese: 8
- Total: \( 5 + 8 = 13 \)

8. How many people ordered pizzas with Cheese?
- People who ordered pizzas with Cheese are in the entire Cheese circle.
- This includes:
- Only Cheese: 12
- Mushrooms and Cheese: 8
- Total: \( 12 + 8 = 20 \)

9. How many people ordered pizzas with just Mushrooms?
- This is the part of the Mushrooms circle that does not overlap with the Cheese circle.
- Value: 5

10. How many people ordered pizzas with both Mushrooms and Cheese?
- This is the intersection of the Mushrooms and Cheese circles.
- Value: 8

11. How many people ordered no pizzas?
- The total number of people at the party is 33.
- People who ordered pizzas are in the union of the Mushrooms and Cheese circles.
- Total people who ordered pizzas:
- Only Mushrooms: 5
- Only Cheese: 12
- Mushrooms and Cheese: 8
- Total: \( 5 + 12 + 8 = 25 \)
- People who ordered no pizzas: \( 33 - 25 = 8 \)

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Problem 3: Venn Diagram for Travel (Paris, France)

#### Venn Diagram:
- Paris: 2 (only Paris), 6 (Paris and France)
- France: 8 (only France), 6 (Paris and France)
- Total surveyed: 19

#### Questions:

12. How many people traveled to just France?
- This is the part of the France circle that does not overlap with the Paris circle.
- Value: 8

13. How many people traveled to France?
- People who traveled to France are in the entire France circle.
- This includes:
- Only France: 8
- Paris and France: 6
- Total: \( 8 + 6 = 9 \)

14. How many people traveled to both Paris and France?
- This is the intersection of the Paris and France circles.
- Value: 6

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Final Answers:

1. An Xbox: \( \boxed{21} \)
2. An Xbox and a PS3: \( \boxed{5} \)
3. At least two consoles: \( \boxed{16} \)
4. An Xbox or a Wii: \( \boxed{25} \)
5. An Xbox and PS3, but not a Wii: \( \boxed{5} \)
6. No console: \( \boxed{12} \)

7. Mushrooms: \( \boxed{13} \)
8. Cheese: \( \boxed{20} \)
9. Just Mushrooms: \( \boxed{5} \)
10. Both Mushrooms and Cheese: \( \boxed{8} \)
11. No pizzas: \( \boxed{8} \)

12. Just France: \( \boxed{8} \)
13. France: \( \boxed{9} \)
14. Both Paris and France: \( \boxed{6} \)