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.