Set Theory Reasoning Problems

Set Theory Reasoning Problems

Set Theory Reasoning Problems

1. 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}?
{1, 2, 3, 6, 7, 8}
{4, 5, 9, 10}
{1, 2, 3, 4, 5, 6, 7, 8}
{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}?
{1, 2, 3, 6, 7, 8}
{4, 5, 9, 10}
{1, 2, 3, 4, 5, 6, 7, 8}
{9, 10}
3. In a school of 1000 students, 600 study math, 500 study science, and 300 study both. How many students study neither math nor science?
100
200
300
400
4. In a class of 50 students, 25 study French, 30 study German, and 10 study both. How many students study neither French nor German?
5
10
15
20
5. 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}
{1, 2, 3, 4, 5, 6, 7, 8}
{4, 5}
{1, 2, 3, 4, 5}
6. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is |A ∪ B| + |A ∩ B|?
8
9
10
11
7. 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}?
{1, 2, 3, 6, 7, 8}
{4, 5}
{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 |A' ∩ B'| in the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?
1
2
3
4
9. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, what is (A ∪ B)'?
{1, 2, 3}
{6, 7, 8}
{9, 10}
{}
10. In a survey of 200 people, 140 like apples, 120 like oranges, and 80 like both. How many people like neither apples nor oranges?
10
20
30
40
Questions Answered: 0/10