Set Theory Reasoning Problems

1. 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}

{4, 5}

{1, 2, 3, 4, 5}

{4, 5, 6, 7, 8}

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}?

6

7

8

9

4. 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'?

{1, 3, 5, 7, 9}

{2, 4, 6, 8, 10}

{1, 2, 3, 4, 5}

{6, 7, 8, 9, 10}

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

8

9

10

11

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

{4, 5, 9, 10}

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

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

{9, 10}

7. 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}?

{9, 10}

{1, 2, 3}

{4, 5}

{6, 7, 8}

8. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is |A - B| + |B - A|?

3

5

6

8

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

240

248

252

256

10. 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, 9, 10}

{6, 7, 8, 9, 10}

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

{4, 5}