Union intersection and complement of sets - Question Bank

1. The elements that are in A and also in B are represented by:
A) A ∩ B
B) A ∪ B
C) A - B
D) A Δ B
2. The elements that are in A or in B or in both are represented by:
A) A ∩ B
B) A - B
C) A ∪ B
D) A Δ B
3. If A ⊆ B, then A ∩ B is equal to:
A) A
B) B
C) ∅
D) U
4. Let U = {a, b, c, d, e} and A = {a, c}. What is A' ∩ A?
A) {b, d, e}
B) {a, c}
C) ∅
D) U
5. If A = {1, 2, 3} and B = {1, 2, 3}, what is A ∩ B?
A) {1, 2, 3}
B) {1, 2}
C) {3}
D) ∅
6. If A = {1, 2, 3} and B = {1, 2, 3}, what is A ∪ B?
A) {1, 2, 3}
B) {1, 2}
C) {3}
D) ∅
7. Which law states that (A ∩ B)' = A' ∪ B'?
A) De Morgan's Law
B) Distributive Law
C) Associative Law
D) Commutative Law
8. Which law states that (A ∪ B)' = A' ∩ B'?
A) Distributive Law
B) Commutative Law
C) Associative Law
D) De Morgan's Law
9. Which law states that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?
A) De Morgan's Law
B) Distributive Law
C) Associative Law
D) Commutative Law
10. If U is the universal set and A is any set, then A ∩ U is:
A) A
B) U
C) ∅
D) A'
11. If U is the universal set and A is any set, then A ∪ U is:
A) A
B) U
C) ∅
D) A'
12. If A and B are two sets such that A ∩ B = A, then which of the following is true?
A) B ⊆ A
B) A ⊆ B
C) A = B
D) A ∪ B = ∅
13. Using the sets from the previous question, what is A ∪ B?
A) {E, U, A, I, O}
B) {E, D, U, C, A, T, I, O, N}
C) {E, D, U, C, A, T, I, O, N}
D) {E, U, A, I, O, D, C, T, N}
14. If A = {vowels in the English alphabet} and B = {letters in the word 'EDUCATION'}, what is A ∩ B?
A) {E, U, A, I, O}
B) {E, D, U, C, A, T, I, O, N}
C) {E, U, A, I, O}
D) {E, D, C, T, N}
15. The formula for the number of elements in the union of two sets is given by:
A) |A ∪ B| = |A| + |B|
B) |A ∪ B| = |A| + |B| - |A ∩ B|
C) |A ∪ B| = |A| + |B| + |A ∩ B|
D) |A ∪ B| = |A| - |B|
16. What is the relationship between A - B and B - A?
A) A - B = B - A
B) (A - B) ∪ (B - A) = A Δ B
C) (A - B) ∩ (B - A) = A ∪ B
D) (A - B) ∩ (B - A) = A ∩ B
17. If A ∪ B = B, this implies:
A) A ⊆ B
B) B ⊆ A
C) A = B
D) A and B are disjoint
18. If A ∩ B = A, this implies:
A) A ⊆ B
B) B ⊆ A
C) A = B
D) A and B are disjoint
19. Let U = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5}. What is the number of elements in A ∪ A'?
A) 3
B) 6
C) 0
D) 9
20. Using the sets from the previous question, what is A ∪ B?
A) {2, 3, 5, 7}
B) {1, 3, 5, 7, 9}
C) {2, 3, 5, 7, 1, 9}
D) {1, 2, 3, 5, 7, 9}
21. If A = {prime numbers less than 10} and B = {odd numbers less than 10}, what is A ∩ B?
A) {2, 3, 5, 7}
B) {1, 3, 5, 7, 9}
C) {3, 5, 7}
D) {2, 3, 5, 7, 9}
22. Which property relates intersection and union in the form A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?
A) Commutative Property
B) Associative Property
C) Distributive Property
D) Identity Property
23. Which property relates union and intersection in the form A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)?
A) Commutative Property
B) Associative Property
C) Distributive Property
D) Idempotent Property
24. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is A Δ B?
A) {3, 4}
B) {1, 2, 5, 6}
C) {1, 2, 3, 4, 5, 6}
D) {1, 5, 6}
25. The symmetric difference of two sets A and B, denoted by A Δ B, is defined as:
A) (A ∪ B) - (A ∩ B)
B) A ∩ B
C) A ∪ B
D) A' ∪ B'
26. Let A = {1, 2, 3} and B = {3, 4, 5}. What is the set difference B - A?
A) {1, 2}
B) {3}
C) {4, 5}
D) {1, 2, 3, 4, 5}
27. Let A = {1, 2, 3} and B = {3, 4, 5}. What is the set difference A - B?
A) {1, 2}
B) {3}
C) {4, 5}
D) {1, 2, 3, 4, 5}
28. If A and B are any two sets, which of the following is always true?
A) A ∪ B = A ∩ B
B) A ∩ B ⊆ A ∪ B
C) A ∪ B ⊆ A ∩ B
D) A ∩ B = ∅
29. The complement of the complement of a set A is:
A) ∅
B) U
C) A'
D) A
30. If |A ∪ B| = 10, |A| = 6, and |B| = 7, what is |A ∩ B|?
A) 1
B) 3
C) 13
D) 16
31. If |A| = 5, |B| = 7, and |A ∩ B| = 3, what is |A ∪ B|?
A) 15
B) 9
C) 12
D) 8
32. Let U = {1, 2, 3, 4, 5} and A = {1, 2}. What is the number of elements in A'?
A) 2
B) 3
C) 5
D) 0
33. Using the sets from the previous question, what is A ∩ B?
A) {4}
B) {1, 2, 3}
C) {5, 6}
D) {1, 2, 3, 4, 5, 6}
34. If A = {x | x is a natural number less than 5} and B = {x | x is a natural number greater than 3 and less than 7}, what is A ∪ B?
A) {1, 2, 3, 4, 5, 6}
B) {4, 5, 6}
C) {1, 2, 3}
D) {1, 2, 3, 4, 5, 6, 7}
35. The distributive property of union over intersection states that:
A) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
B) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
C) A ∪ B = B ∪ A
D) A ∩ B = B ∩ A
36. The distributive property of intersection over union states that:
A) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
B) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
C) A ∪ B = B ∪ A
D) A ∩ B = B ∩ A
37. Let U = {all integers} and A = {even integers}. What is A'?
A) {even integers}
B) {odd integers}
C) {prime integers}
D) {composite integers}
38. If A = {apple, banana, cherry} and B = {banana, date, fig}, what is A ∩ B?
A) {apple, banana, cherry, date, fig}
B) {apple, cherry}
C) {banana}
D) {date, fig}
39. If A = {1, 3, 5} and B = {2, 4, 6}, what is A ∪ B?
A) {1, 2, 3, 4, 5, 6}
B) {1, 3, 5}
C) {2, 4, 6}
D) ∅
40. For any set A, A ∩ A' is equal to:
A) A
B) A'
C) U (universal set)
D) ∅ (empty set)
41. For any set A, A ∪ A' is equal to:
A) A
B) A'
C) U (universal set)
D) ∅ (empty set)
42. Which of the following is NOT a property of set intersection?
A) A ∩ ∅ = ∅
B) A ∩ A = A
C) A ∩ U = A
D) A ∩ B = A ∪ B
43. Which of the following is NOT a property of set union?
A) A ∪ ∅ = A
B) A ∪ A = A
C) A ∪ U = U
D) A ∪ B = A ∩ B
44. What is (A ∩ B)'?
A) A' ∪ B'
B) A' ∩ B'
C) A ∪ B
D) A ∩ B
45. What is (A ∪ B)'?
A) A' ∪ B'
B) A' ∩ B'
C) A ∩ B
D) A ∪ B
46. If A ∩ B = ∅, then sets A and B are called:
A) Equal sets
B) Disjoint sets
C) Subset
D) Superset
47. If A ⊆ B, then A ∪ B is equal to:
A) A
B) B
C) ∅ (empty set)
D) U (universal set)
48. The intersection of two sets A and B, denoted by A ∩ B, contains elements that are:
A) In set A only
B) In set B only
C) In both set A and set B
D) In either set A or set B or both
49. Which property states that for any two sets A and B, A ∪ B = B ∪ A?
A) Associative Property
B) Distributive Property
C) Commutative Property of Union
D) Idempotent Property
50. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set and A = {2, 4, 6, 8}. What is the complement of A (A')?
A) {1, 3, 5, 7, 9}
B) {2, 4, 6, 8}
C) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
D) {}
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