25 Multiple choice questions from sets

1. Which of the following is an example of a finite set?
   a) The set of prime numbers
   b) The set of natural numbers
   c) The set of even numbers less than 20
   d) The set of real numbers

2. If A = {2, 4, 6, 8} and B = {4, 8, 12, 16}, what is A ∩ B?
   a) {2, 4, 6, 8}
   b) {4, 8}
   c) {12, 16}
   d) {2, 6}

3. What is the cardinality of the set A = {a, b, c, d, e}?
   a) 3
   b) 4
   c) 5
   d) 6

4. A set that contains all elements under consideration is called:
   a) Null set
   b) Universal set
   c) Subset
   d) Power set

5. If A ⊆ B and B ⊆ C, then:
   a) A = C
   b) A ⊆ C
   c) C ⊆ A
   d) A ∩ B = C

6. Which of the following is a null set?
   a) {0}
   b) {}
   c) {1, 2, 3}
   d) {∅}

7. The power set of {1, 2, 3} has how many elements?
   a) 4
   b) 6
   c) 8
   d) 10

8. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B is:
   a) {1, 2, 3, 4, 5}
   b) {3, 4, 5}
   c) {1, 2, 3}
   d) {1, 2, 5}

9. What is the complement of the universal set?
   a) The null set
   b) The set itself
   c) A subset of the universal set
   d) Cannot be determined

10. The number of subsets of a set with n elements is:
    a) 2^n
    b) n^2
    c) n!
    d) 2n

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11. If A = {x | x is an even number} and B = {x | x is a multiple of 3}, what is A ∩ B?
    a) {6, 12, 18, ...}
    b) {2, 4, 6, ...}
    c) {3, 6, 9, ...}
    d) {}

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12. Which of the following sets is countable?
    a) The set of real numbers
    b) The set of natural numbers
    c) The set of irrational numbers
    d) The set of points in a plane

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13. The difference of sets A and B, denoted as A - B, contains:
    a) Elements in A but not in B
    b) Elements in B but not in A
    c) Elements in both A and B
    d) The universal set

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14. The number of elements in a power set of {1, 2, 3, 4} is:
    a) 4
    b) 8
    c) 16
    d) 32

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15. If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B is:
    a) {1, 2, 3, 4, 5}
    b) {3}
    c) {1, 2}
    d) {}

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16. A set with exactly one element is called a:
    a) Power set
    b) Singleton set
    c) Universal set
    d) Finite set

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17. If n(U) = 50, n(A) = 30, and n(B) = 25, and n(A ∩ B) = 10, then n(A ∪ B) is:
    a) 45
    b) 50
    c) 55
    d) 30

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18. A set that contains no elements is called a:
    a) Finite set
    b) Infinite set
    c) Null set
    d) Singleton set

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19. If A ∩ B = {} and A ∪ B = {1, 2, 3, 4, 5}, then A and B are:
    a) Equal sets
    b) Proper subsets
    c) Disjoint sets
    d) Infinite sets

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20. If n(A) = 6, how many subsets does A have?
    a) 12
    b) 32
    c) 64
    d) 128

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21. If A = {1, 2, 3} and B = {3, 4, 5}, what is A × B (Cartesian product)?
    a) {(1,3), (2,4), (3,5)}
    b) {(1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,3), (3,4), (3,5)}
    c) {(1,1), (2,2), (3,3)}
    d) {1, 2, 3, 4, 5}

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22. The set of vowels in the English alphabet is an example of:
    a) Finite set
    b) Infinite set
    c) Singleton set
    d) Null set

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23. If A and B are two sets such that A ⊆ B and B ⊆ A, then:
    a) A and B are equal
    b) A and B are disjoint
    c) A is a subset of B
    d) B is a subset of A

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24. If the universal set is U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {2, 4, 6}, what is A'?
    a) {1, 3, 5, 7, 8}
    b) {2, 4, 6}
    c) {2, 3, 4, 5}
    d) {}

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25. Which of the following is always true for any set A?
    a) A ∩ A' = A
    b) A ∪ A' = U
    c) A - A = U
    d) A ⊆ A'

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Answers

1) c 2) b 3) c 4) b 5) b 6) b 7) c 8) a 9) a 10) a

11) a 12) b 13) a 14) c 15) b 

16) b 17) a 18) c 19) c

20) c 21)b 22) a 23) a 24) a 25) b

Comment if answer is wrong.