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Questions and Answers
What is the relationship between sets A = {1, 2, 5, 10} and B = {1, 2, 4, 5, 10, 20}?
What is the relationship between sets A = {1, 2, 5, 10} and B = {1, 2, 4, 5, 10, 20}?
- A is a proper subset of B (correct)
- B is a proper subset of A
- A is a superset of B
- A is equal to B
Which of the following statements is true about sets C = {x | x is a natural number less than 10} and D = {1, 2, 4, 8}?
Which of the following statements is true about sets C = {x | x is a natural number less than 10} and D = {1, 2, 4, 8}?
- C is equal to D
- C and D have no elements in common
- D is a proper subset of C (correct)
- C is a proper subset of D
What is the relationship between sets E = {1, 2} and F = {x | 0 < x < 3, x ∈ Z}?
What is the relationship between sets E = {1, 2} and F = {x | 0 < x < 3, x ∈ Z}?
- E and F are disjoint sets
- F is a proper subset of E
- E is a proper subset of F (correct)
- E and F are equal
Which set represents the universal set for A = {2, 4, 6}, B = {1, 3, 7, 9, 11}, and C = {4, 8, 11}?
Which set represents the universal set for A = {2, 4, 6}, B = {1, 3, 7, 9, 11}, and C = {4, 8, 11}?
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Which of the following is a true statement regarding the relationship of sets A, B, C, and the universal set U?
Which of the following is a true statement regarding the relationship of sets A, B, C, and the universal set U?
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Study Notes
Set Relationships
- For sets A = {1, 2, 5, 10} and B = {1, 2, 4, 5, 10, 20}: A is a subset of B (A ⊆ B) because all elements of A are contained in B.
- For sets C = {x | x is a natural number less than 10} and D = {1, 2, 4, 8}: D is a subset of C (D ⊆ C) as all elements in D are natural numbers less than 10.
- For sets E = {1, 2} and F = {x | 0 < x < 3, x ∈ Z}: E and F are equal (E = F) since both sets contain the same elements, specifically {1, 2}.
Universal Set and Subsets
- For sets A = {2, 4, 6}, B = {1, 3, 7, 9, 11}, and C = {4, 8, 11}: The universal set U can be defined as the union of all elements from A, B, and C: U = {1, 2, 3, 4, 6, 7, 8, 9, 11}.
- Set A is a subset of U (A ⊆ U), set B is a subset of U (B ⊆ U), and set C is a subset of U (C ⊆ U).
Operations on Sets
- New sets can be generated through operations such as union, intersection, and difference, utilizing already defined sets, expanding the capabilities of set theory.
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