Math Problem Statement
U= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} A ={0, 3, 6, 9, 12} B = {2, 4, 6, 8, 10, 12, 14} C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} answer the odd numbers only
Solution
Here are the results for the odd-numbered questions:
- 31. (A ∩ C)' = {0, 1, 2, 4, 5, 7, 8, 10, 11, 12, 13, 14}
- 33. A' ∩ (B ∪ C)' = {11, 13}
- 35. C' ∩ (A ∪ B)' = {11, 13}
- 37. (A ∩ B)' ∪ (B ∩ C)' = {0, 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14}
- 39. (A' ∪ B)' ∩ (U ∪ C') = {0, 3, 9}
Let me know if you want more details about any of these problems.
Here are some related questions to expand your understanding:
- How do we compute set complements and why are they important?
- Can you explain how the intersection and union of sets differ in logical terms?
- How would the results change if we altered the universal set ?
- What is the role of De Morgan's laws in set theory?
- Can you show how set operations can be applied in real-world problem solving?
Tip: Always keep track of the universal set , as it is key to calculating complements correctly.
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Math Problem Analysis
Mathematical Concepts
Set Theory
Union
Intersection
Complement
Formulas
Union of Sets: A ∪ B = {x : x ∈ A or x ∈ B}
Intersection of Sets: A ∩ B = {x : x ∈ A and x ∈ B}
Complement of Set: A' = {x : x ∉ A}
De Morgan's Laws: (A ∩ B)' = A' ∪ B' and (A ∪ B)' = A' ∩ B'
Theorems
De Morgan's Laws
Basic Set Operations
Suitable Grade Level
Grades 9-12