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Power Sets and Subsets: Unraveling the Structure of Sets

Power Sets and Subsets: Unraveling the Structure of Sets

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

Given a set A with n elements, how many subsets does A have?

  1. 2^n
  2. n^2
  3. n!
  4. n
Question 2 Multiple Choice (Single Answer)

If A and B are two sets, which of the following is always true?

  1. A ∪ B ⊆ P(A ∪ B)
  2. A ∩ B ⊆ P(A ∩ B)
  3. A - B ⊆ P(A - B)
  4. A × B ⊆ P(A × B)
Question 3 Multiple Choice (Single Answer)

What is the cardinality of the power set of an empty set?

  1. 0
  2. 1
  3. 2
  4. ∞
Question 4 Multiple Choice (Single Answer)

If A is a finite set with n elements, how many subsets of A have exactly k elements?

  1. n choose k
  2. n permute k
  3. n combine k
  4. n subtract k
Question 5 Multiple Choice (Single Answer)

Which of the following is a proper subset of the set {1, 2, 3, 4, 5}?

  1. {1, 2, 3, 4, 5}
  2. {1, 2, 3}
  3. {1, 3, 5}
  4. {2, 4, 5}
Question 6 Multiple Choice (Single Answer)

If A and B are two sets, which of the following is always true?

  1. P(A ∩ B) = P(A) ∩ P(B)
  2. P(A ∪ B) = P(A) ∪ P(B)
  3. P(A - B) = P(A) - P(B)
  4. P(A × B) = P(A) × P(B)
Question 7 Multiple Choice (Single Answer)

What is the cardinality of the power set of a set with n elements?

  1. n
  2. 2^n
  3. n!
  4. ∞
Question 8 Multiple Choice (Single Answer)

If A is a set with n elements, how many subsets of A have an even number of elements?

  1. 2^(n-1)
  2. 2^n
  3. n choose (n/2)
  4. n permute (n/2)
Question 9 Multiple Choice (Single Answer)

Which of the following is a subset of the set {1, 2, 3, 4, 5}?

  1. {1, 2, 3, 4, 5}
  2. {1, 3, 5}
  3. {2, 4}
  4. {6, 7, 8}
Question 10 Multiple Choice (Single Answer)

If A and B are two sets, which of the following is always true?

  1. P(A ∪ B) = P(A) ∪ P(B)
  2. P(A ∩ B) = P(A) ∩ P(B)
  3. P(A - B) = P(A) - P(B)
  4. P(A × B) = P(A) × P(B)
Question 11 Multiple Choice (Single Answer)

What is the cardinality of the power set of a set with 3 elements?

  1. 3
  2. 6
  3. 8
  4. 9
Question 12 Multiple Choice (Single Answer)

If A is a set with n elements, how many subsets of A have an odd number of elements?

  1. 2^(n-1)
  2. 2^n
  3. n choose (n/2)
  4. n permute (n/2)
Question 13 Multiple Choice (Single Answer)

Which of the following is a proper subset of the set {1, 2, 3, 4, 5}?

  1. {1, 2, 3, 4, 5}
  2. {1, 2, 3}
  3. {1, 3, 5}
  4. {2, 4, 5}
Question 14 Multiple Choice (Single Answer)

If A and B are two sets, which of the following is always true?

  1. P(A ∩ B) = P(A) ∩ P(B)
  2. P(A ∪ B) = P(A) ∪ P(B)
  3. P(A - B) = P(A) - P(B)
  4. P(A × B) = P(A) × P(B)
Question 15 Multiple Choice (Single Answer)

What is the cardinality of the power set of a set with n elements?

  1. n
  2. 2^n
  3. n!
  4. ∞
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