MSTE-1 (SET THEORY)

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Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

1. Determine A ∪ B.

• a. {1, 2, 3, 4, 5, 6, 7, 8, 9}
• b. {1, 4, 5, 8, 9}
• c. {1, 2, 3, 5, 6, 7, 8, 9}
• d. {1, 2, 3, 4, 5, 6, 8, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

2. Determine A ∩ B.

• a. {5, 8}
• b. {7}
• c. {3, 4, 5}
• d. {5, 8, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

3. Determine A'.

• a. {2, 3, 5, 6, 8}
• b. {1, 4, 5, 8, 9}
• c. {2, 3, 6, 7}
• d. {2, 3, 6, 7, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

4. Determine (A ∪ B)'.

• a. {5}
• b. {4}
• c. {3}
• d. {7}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

5. Determine (A ∩ B)'.

• a. {1, 2, 3, 5, 6, 8}
• b. {1, 2, 3, 4, 6, 7, 9}
• c. {1, 2, 3, 6, 7, 8, 9}
• d. {1, 2, 3, 6, 7, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

6. Determine (A\B)'.

• a. {1, 5, 9}
• b. {1, 6, 9}
• c. {1, 2, 9}
• d. {1, 4, 9}

7. Which of the following represents the set equivalent to A′ ∪ B′.

• a. A ∪ B
• b. A ∩ B
• c. (A ∪ B)'
• d. (A ∩ B)'

8. Which of the following represents the set equivalent to (A ∪ B ∪ C) ∩ B.

• a. B
• b. A
• c. A ∩ B
• d. A ∪ B

9. Which of the following represents the set equivalent to (A ∪ B) ∩ (A ∩ B).

• a. A + B
• b. A - B
• c. A ∩ B
• d. A ∪ B

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

10. How many people like only pizza?

• a. 25
• b. 15
• c. 60
• d. 20

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

11. How many people like only pasta?

• a. 25
• b. 15
• c. 55
• d. 20

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

12. How many people like only burgers?

• a. 25
• b. 15
• c. 50
• d. 20

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

13. How many people like exactly two of the three foods?

• a. 25
• b. 20
• c. 15
• d. 30

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

14. How many people like all three foods?

• a. 25
• b. 20
• c. 15
• d. 30

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

15. How many students like only basketball?

• a. 13
• b. 14
• c. 15
• d. 16

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

16. How many students like only football?

• a. 3
• b. 4
• c. 5
• d. 6

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

17. How many students like neither basketball nor football?

• a. 6
• b. 8
• c. 9
• d. 7

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

18. How many students like either basketball or football?

• a. 21
• b. 41
• c. 31
• d. 11

At a beverage counter, four types of drinks are available: Mocha, Chocolate, Coffee, and Vanilla. The shop recorded the following orders:

30 customers ordered Mocha
29 ordered Chocolate
23 ordered Coffee
26 ordered Vanilla

Some customers ordered more than one drink:
18 ordered both Mocha and Chocolate
9 ordered both Mocha and Coffee
15 ordered both Mocha and Vanilla
15 ordered both Chocolate and Coffee
14 ordered both Chocolate and Vanilla
14 ordered both Coffee and Vanilla

In addition:
6 customers ordered Mocha, Chocolate, and Coffee
9 ordered Mocha, Chocolate, and Vanilla
7 ordered Mocha, Coffee, and Vanilla
9 ordered Chocolate, Coffee, and Vanilla
4 customers ordered all four drinks

19. Assuming each customer placed at least one order, how many unique customers visited the shop?

• a. A + B
• b. A - B
• c. A ∩ B
• d. A ∪ B

At a beverage counter, four types of drinks are available: Mocha, Chocolate, Coffee, and Vanilla. The shop recorded the following orders:

30 customers ordered Mocha
29 ordered Chocolate
23 ordered Coffee
26 ordered Vanilla

Some customers ordered more than one drink:
18 ordered both Mocha and Chocolate
9 ordered both Mocha and Coffee
15 ordered both Mocha and Vanilla
15 ordered both Chocolate and Coffee
14 ordered both Chocolate and Vanilla
14 ordered both Coffee and Vanilla

In addition:
6 customers ordered Mocha, Chocolate, and Coffee
9 ordered Mocha, Chocolate, and Vanilla
7 ordered Mocha, Coffee, and Vanilla
9 ordered Chocolate, Coffee, and Vanilla
4 customers ordered all four drinks

20. How many customers ordered exactly one type of drink?

• a. 35
• b. 10
• c. 25
• d. 15

ANSWER KEY:

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