Consider the following statement. For all sets A and B, (A U B) = A°U B. Which sentence below expresses what it means for the statement to be false? (Select all that apply.) O There are sets A and B such that (A U B) + AU BE. O For all sets A, there is a set B such that (A U B) + A U B. O There is a set A such that for all sets B, (AU B) + A° U BC. O For all sets A and B, (A U B) + A U BC. 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 Ø for the empty set.) А, В -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following statement.

For all sets \( A \) and \( B \), \( (A \cup B)^c = A^c \cup B^c \).

Which sentence below expresses what it means for the statement to be false? (Select all that apply.)

- [ ] 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 \( (A \cup B)^c \neq A^c \cup B^c \).
- [ ] There is a set \( A \) such that for all sets \( B \), \( (A \cup B)^c \neq A^c \cup B^c \).
- [ ] For all sets \( A \) and \( B \), \( (A \cup B)^c \neq A^c \cup B^c \).

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 box]

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Transcribed Image Text:Consider the following statement. For all sets \( A \) and \( B \), \( (A \cup B)^c = A^c \cup B^c \). Which sentence below expresses what it means for the statement to be false? (Select all that apply.) - [ ] 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 \( (A \cup B)^c \neq A^c \cup B^c \). - [ ] There is a set \( A \) such that for all sets \( B \), \( (A \cup B)^c \neq A^c \cup B^c \). - [ ] For all sets \( A \) and \( B \), \( (A \cup B)^c \neq A^c \cup B^c \). 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 box] Need Help? - Read It - Watch It
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