Let sets A and B be subsets of S, where:
Set A = {1, 3, 4, 5, 7, 11, 12, 16, 17}
Set B = {3, 4, 5, 7,9, 10,11, 13, 16, 17, 20}
Find the following:
LIST the elements in the set (An B°):
(An B°) - [
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (Bn A°):
(BnA) - [

Let's start by finding the sets \( A^c \) and \( B^c \), which are the complements of sets \( A \) and \( B \) in \( S \) (assuming \( S \) is a universal set that contains all possible elements relevant to the problem).

### 1. Finding \( A \cap B^c \):
- \( A \) is: \( \{1, 3, 4, 5, 7, 11, 12, 16, 17\} \)
- \( B \) is: \( \{3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 20\} \)
  
To find \( A \cap B^c \), we first find \( B^c \), the complement of \( B \), which consists of elements in \( S \) that are not in \( B \). We then find the intersection of \( A \) with \( B^c \).

However, since \( S \) is not specified, we can determine \( B^c \) relative to \( A \cup B \). So, let's first list the elements of \( A \cup B \):
- \( A \cup B = \{1, 3, 4, 5, 7, 9, 10, 11, 12, 13, 16, 17, 20\} \)

Now, \( B^c \) relative to \( A \cup B \) will be the elements of \( A \cup B \) that are not in \( B \):
- \( B^c = \{1, 12\} \)

Now, we find \( A \cap B^c \), which is the intersection of \( A \) with \( B^c \):
- \( A \cap B^c = \{1, 12\} \)

### 2. Finding \( B \cap A^c \):
To find \( B \cap A^c \), we first find \( A^c \), the complement of \( A \) relative to \( A \cup B \), which consists of elements in \( A \cup B \) that are not in \( A \):
- \( A^c = \{9, 10, 13, 20\} \)

Now, we find \( B \cap A^c \), which is the intersection of \( B \) with \( A^c \):
- \( B \cap A^c = \{9, 10, 13, 20\} \)

### Final Results:
- \( A \cap B^c = \{1, 12\} \)
- \( B \cap A^c = \{9, 10, 13, 20\} \)

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Do you want more details or have any further questions?

Here are five related questions:
1. What is the union of \( A \) and \( B \)?
2. What is the complement of \( A \cup B \) relative to \( S \), if \( S \) is known?
3. What is the difference \( A - B \) (elements in \( A \) but not in \( B \))?
4. How do you find the symmetric difference \( A \Delta B \)?
5. What is the intersection of \( A \cup B \) with another set \( C \), if \( C \) is provided?

**Tip:** When working with complements of sets, always be clear about the universal set \( S \) you're working in, as it determines the elements that belong to the complements.

Let sets A and B be subsets of S, where: Set A = {1, 3, 4, 5, 7, 11, 12, 16, 17} Set B = {3, 4, 5, 7, 9, 10, 11, 13, 16, 17, 20} Find the following: LIST the elements in the set (A ∩ B^c): (A ∩ B^c) - [Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set (B ∩ A^c): (B ∩ A^c) - [

Learn how to solve set theory problems involving intersection and complements of sets A and B. This problem covers core set operations and uses De Morgan's laws to find the solutions. Suitable for students in Grades 9-12.

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