Sets:

1. Q: If A = {1, 2, 3} and B = {3, 4, 5}, find A ∪ B.
   Answer: {1, 2, 3, 4, 5} 

2. Q: If A = {1, 2, 3} and B = {3, 4, 5}, find A ∩ B.
   Answer: {3}

3. Q: If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, find A – B.
   Answer: {1, 2}

4. Q: What is the cardinality of the set {a, e, i, o, u}?
   Answer: 5

5. Q: If A = {1, 2, 3}, how many subsets does A have?
   Answer: 2^3=8

6. Q: If A = {1, 2, 3, 4} and B = {2, 4, 6}, find A ∆ B (symmetric difference).
   Answer: {1, 3, 6} 

7. Q: If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, find A′ (complement of A).
   Answer: {1, 3, 5}

8. Q: If A ⊆ B and B = {1, 2, 3}, which of the following can be A?
   Answer: Any subset, e.g., {1, 2}

9. Q: If A = {x x is an even number < 10}, list A.
   Answer: {2, 4, 6, 8}

10. Q: If A = {1, 2}, B = {2, 3}, and C = {3, 4}, find (A ∪ B) ∩ C.
    Answer: {3}

11. Q: In a class of 50 students, 30 like Math, 25 like Science, and 10 like both. How many like only Math?
    Answer: 30 – 10 = 20 

12. Q: In a group of 100 people, 60 like tea, 50 like coffee, and 20 like both. How many like neither?
    Answer: 100 – (60 + 50 – 20) = 10

13. Q: If A = {1, 2, 3}, B = {3, 4, 5}, and C = {5, 6}, find A ∪ (B ∩ C).
    Answer: {1, 2, 3, 5}

14. Q: If A = {1, 2, 3, 4} and B = {2, 4, 6}, find (A ∩ B)′ in U = {1, 2, 3, 4, 5, 6}.
    Answer: {1, 3, 5, 6}

15. Q: In a survey, 70 people liked cricket, 60 liked football, and 40 liked both. How many liked only one sport?
    Answer: (70 – 40) + (60 – 40) = 50

16. Q: If A ∪ B = A ∩ B, what can you say about A and B?
    Answer: A = B 

17. Q: If A = {x ∈ N x < 10} and B = {x ∈ N x is even, x < 10}, find A – B.
    Answer: {1, 3, 5, 7, 9}

18. Q: If n(A) = 20, n(B) = 15, and n(A ∩ B) = 5, find n(A ∪ B).
    Answer: 20 + 15 – 5 = 30

19. Q: If A = {1, 2, 3}, B = {2, 3, 4}, and C = {3, 4, 5}, find A ∩ B ∩ C.
    Answer: {3}

20. Q: In a class of 60 students, 35 like English, 30 like Hindi, and 20 like both. How many like neither?
    Answer: 60 – (35 + 30 – 20) = 15