А - (ВnС) %3D(А — В) n (А — С)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
prove or disprove using any valid method of proof for sets
![The formula presented is:
\[ A - (B \cap C) = (A - B) \cap (A - C) \]
This expression relates to set theory and describes a property of set difference and intersection.
- **Left Side:**
- **\(A - (B \cap C)\):** This represents the set of elements that are in set \(A\) but not in the intersection of sets \(B\) and \(C\).
- **Right Side:**
- **\((A - B) \cap (A - C)\):** This expression indicates the intersection of two sets:
- \(A - B\): The set of elements that are in \(A\) but not in \(B\).
- \(A - C\): The set of elements that are in \(A\) but not in \(C\).
- By taking the intersection of these two results, we identify the elements that are in \(A\) but not in either \(B\) or \(C\).
This equation demonstrates a distributive property of set operations, similar to distribution in algebra, showcasing how subtraction (or difference) in sets interacts with intersection operations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e824278-0cf8-4697-a6ac-3768c642cb77%2F4bd0ef56-28e0-4ad4-9ea3-158c252f59b8%2Fd2w7lnn_processed.png&w=3840&q=75)
Transcribed Image Text:The formula presented is:
\[ A - (B \cap C) = (A - B) \cap (A - C) \]
This expression relates to set theory and describes a property of set difference and intersection.
- **Left Side:**
- **\(A - (B \cap C)\):** This represents the set of elements that are in set \(A\) but not in the intersection of sets \(B\) and \(C\).
- **Right Side:**
- **\((A - B) \cap (A - C)\):** This expression indicates the intersection of two sets:
- \(A - B\): The set of elements that are in \(A\) but not in \(B\).
- \(A - C\): The set of elements that are in \(A\) but not in \(C\).
- By taking the intersection of these two results, we identify the elements that are in \(A\) but not in either \(B\) or \(C\).
This equation demonstrates a distributive property of set operations, similar to distribution in algebra, showcasing how subtraction (or difference) in sets interacts with intersection operations.
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