Set Theory Reasoning Problems

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

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?

3. 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. In a survey of 300 people, 180 like coffee, 150 like tea, and 60 like both. How many people like either coffee or tea but not both?

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}?

6. In a group of 100 people, 70 like chocolate, 60 like vanilla, and 40 like both. How many people like neither chocolate nor vanilla?

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

8. If A = {1, 2, 3} and B = {x | x is an even number less than 7}, what is P(A ∩ B)?

9. In a class of 50 students, 30 like mathematics, 20 like physics, and 10 like both mathematics and physics. How many students like neither mathematics nor physics?

10. In a group of 100 people, 70 speak English, 45 speak French, and 15 speak both. How many people speak neither English nor French?