Set Theory Reasoning Problems

1. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is (A ∪ B) - (A ∩ B)?

{1, 2, 5, 6}

{3, 4}

{1, 2, 3, 4, 5, 6}

{}

2. In a survey of 200 people, 120 like pizza, 80 like burgers, and 40 like both. How many people like either pizza or burgers but not both?

80

120

160

200

3. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is |A' ∩ B'| in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

1

2

3

4

4. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is (A' ∪ B') in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

{1, 2, 3, 6, 7, 8, 9, 10}

{9, 10}

{1, 2, 3, 9, 10}

{6, 7, 8, 9, 10}

5. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is (A' ∩ B')' in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

{1, 2, 3, 4, 5, 6, 7, 8}

{9, 10}

{4, 5}

{1, 2, 3, 6, 7, 8}

6. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is |P(A ∪ B)|?

64

128

256

512

7. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is the universal set and A = {2, 4, 6, 8, 10}, what is A ∩ A'?

{1, 3, 5, 7, 9}

{2, 4, 6, 8, 10}

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

{}

8. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is |P(A) ∪ P(B)|?

48

56

60

64

9. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is |P(A) × P(B)|?

512

1024

2048

4096

10. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is (A ∪ B) ∆ (A ∩ B)?

{1, 2, 3, 6, 7, 8}

{4, 5}

{1, 2, 3, 4, 5, 6, 7, 8}

{1, 2, 3, 4, 5}