Set Theory Reasoning Problems

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

{1, 2, 3}

{6, 7, 8}

∅ (empty set)

{4, 5}

2. 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}

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

{1, 2, 3}

{4, 5}

{6, 7, 8}

{1, 2, 3, 4, 5}

4. 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}

5. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is the cardinality of A ∪ B?

5

7

8

10

6. In a class of 40 students, 25 play soccer, 20 play basketball, and 10 play both. How many students play either soccer or basketball?

25

30

35

40

7. In a survey of 200 people, 120 like pizza, 100 like pasta, and 60 like both. How many people like either pizza or pasta?

140

150

160

170

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 (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}

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

{1, 2, 3}

{4, 5}

{6, 7, 8}

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