📚Set Theory Multiple-Choice Questions
1. If A={1,2,3,4} and B={3,4,5,6}, then n(A∪ B) is:
A. 4
B. 5
C. 6
D. 8
2. A set has 4 elements. How many subsets does it have?
A. 4
B. 8
C. 12
D. 16
3. If A={1,2,3,4,5} and B={2,4,6}, then A-B is:
A. {2,4}
B. {1,3,5}
C. {1,2,3,4,5,6}
D. {6}
4. In a class of 50 students, 32 study Mathematics, 28 study Physics, and 15 study both subjects. How many students study neither Mathematics nor Physics?
A. 3
B. 5
C. 7
D. 10
5. How many proper subsets does a set with 5 elements have?
A. 16
B. 25
C. 31
D. 32
6. Find the intersection of the intervals [1,5) and (3,7].
A. [3,5]
B. (3,5)
C. [3,5)
D. (3,5]
7. If A={1,2,3} and B={3,4}, then the symmetric difference A△ B is:
A. {3}
B. {1,2,4}
C. {1,2,3,4}
D. {1,2}
8. If A⊆ B, n(A)=3, and n(B)=5, then n(B-A) is:
A. 1
B. 2
C. 3
D. 8
9. If A={a,b} and B={1,2,3}, then n(A× B) is:
A. 5
B. 6
C. 8
D. 9
10. Let U={1,2,…,10}, A be the set of multiples of 2, and B the set of multiples of 3. How many elements are in (A∪ B)'?
A. 2
B. 3
C. 4
D. 5
11. Given that n(A)=40, n(B)=35, n(C)=30, n(A∩ B)=15, n(A∩ C)=12, n(B∩ C)=10, and n(A∩ B∩ C)=5, find n(A∪ B∪ C).
A. 68
B. 70
C. 73
D. 78
12. If A∪ B=A, which of the following must be true?
A. A⊆ B
B. B⊆ A
C. A=B'
D. A∩ B=∅
13. In a universal set U, n(U)=100, n(A)=60, n(B)=45, and n(A∩ B)=20. Find n((A∪ B)').
A. 10
B. 15
C. 20
D. 25
14. Which of the following is equivalent to A'∩ B'?
A. (A∩ B)'
B. (A∪ B)'
C. A∪ B
D. A'∪ B'
15. How many subsets of {1,2,3,4,5,6,7,8} contain both 1 and 2?
A. 16
B. 32
C. 64
D. 128
16. If n(A)=18, n(B)=25, and n(A∪ B)=35, then n(A∩ B) is:
A. 6
B. 8
C. 10
D. 12
17. Let
A={x∈ℤ:-2≤ x≤ 3}
and let B be the set of odd integers. Find n(A∩ B).
A. 2
B. 3
C. 4
D. 5
18. Let A={1,2,{1,2}}. What is n(A)?
A. 2
B. 3
C. 4
D. 5
19. If n(A× B)=12 and n(A)=3, then n(B) is:
A. 3
B. 4
C. 6
D. 9
20. Let A be the set of positive divisors of 12 and B the set of positive divisors of 18. Find n(A∪ B).
A. 6
B. 7
C. 8
D. 10
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