Consider the following statement. For all sets A and B, (A U B)ª= Aª U Bº. Which sentence below expresses what it means for the statement to be false? (Select all that apply.) For all sets A and B, (A U B)C ‡ AC U BC. # There is a set A such that for all sets B, (A U B)C ‡
Consider the following statement. For all sets A and B, (A U B)ª= Aª U Bº. Which sentence below expresses what it means for the statement to be false? (Select all that apply.) For all sets A and B, (A U B)C ‡ AC U BC. # There is a set A such that for all sets B, (A U B)C ‡
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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![**Title: Understanding Set Complements and Union**
**Consider the Following Statement:**
For all sets \( A \) and \( B \), \((A \cup B)^c = A^c \cup B^c\).
**Question:**
Which sentence below expresses what it means for the statement to be false? (Select all that apply.)
- □ For all sets \( A \) and \( B \), \((A \cup B)^c \neq A^c \cup B^c\).
- □ There is a set \( A \) such that for all sets \( B \), \((A \cup B)^c \neq A^c \cup B^c\).
- □ There are sets \( A \) and \( B \) such that \((A \cup B)^c \neq A^c \cup B^c\).
- □ For all sets \( A \), there is a set \( B \) such that \((A \cup B)^c \neq A^c \cup B^c\).
**Exercise:**
Find subsets of \(\{1, 2, 3, 4, 5\}\) which can be used to show that the given statement is false. (Enter the sets as \( A, B \) in a comma-separated list. Use set-roster notation or write EMPTY or \(\emptyset\) for the empty set.)
\( A, B = \) [Input Answer Here]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0e38307-1ade-44bc-b712-aaeda4c58098%2Fc97e8f7a-4071-4f62-aeba-a4444be0abe0%2Fcyndoa_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Set Complements and Union**
**Consider the Following Statement:**
For all sets \( A \) and \( B \), \((A \cup B)^c = A^c \cup B^c\).
**Question:**
Which sentence below expresses what it means for the statement to be false? (Select all that apply.)
- □ For all sets \( A \) and \( B \), \((A \cup B)^c \neq A^c \cup B^c\).
- □ There is a set \( A \) such that for all sets \( B \), \((A \cup B)^c \neq A^c \cup B^c\).
- □ There are sets \( A \) and \( B \) such that \((A \cup B)^c \neq A^c \cup B^c\).
- □ For all sets \( A \), there is a set \( B \) such that \((A \cup B)^c \neq A^c \cup B^c\).
**Exercise:**
Find subsets of \(\{1, 2, 3, 4, 5\}\) which can be used to show that the given statement is false. (Enter the sets as \( A, B \) in a comma-separated list. Use set-roster notation or write EMPTY or \(\emptyset\) for the empty set.)
\( A, B = \) [Input Answer Here]
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