You have defined two sets $A$ and $B$ as subsets of the set $S = \{1, 2, 3, \dots, 20\}$, where:

• $A = \{3, 8, 10, 11, 12, 13, 16, 17, 19\}$
• $B = \{2, 3, 4, 6, 8, 12, 19, 20\}$

Here are some key set operations we can perform with these sets:

1. Union of A and B:

The union $A \cup B$ is the set of all elements that are in either $A$, $B$, or both. This operation combines the elements of both sets without duplication.

$A \cup B = \{2, 3, 4, 6, 8, 10, 11, 12, 13, 16, 17, 19, 20\}$

2. Intersection of A and B:

The intersection $A \cap B$ is the set of all elements that are in both $A$ and $B$.

$A \cap B = \{3, 8, 12, 19\}$

3. Difference $A - B$:

The difference $A - B$ is the set of all elements that are in $A$ but not in $B$.

$A - B = \{10, 11, 13, 16, 17\}$

4. Difference $B - A$:

The difference $B - A$ is the set of all elements that are in $B$ but not in $A$.

$B - A = \{2, 4, 6, 20\}$

5. Symmetric Difference of A and B:

The symmetric difference $A \Delta B$ is the set of elements that are in either $A$ or $B$, but not in both. This can be calculated as $(A - B) \cup (B - A)$.

$A \Delta B = \{2, 4, 6, 10, 11, 13, 16, 17, 20\}$

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Would you like more details or have any questions about these operations?

Here are 5 related questions to explore further:

1. What is the complement of set $A$ in $S$?
2. What is the complement of set $B$ in $S$?
3. What is the cardinality (size) of each set: $A$, $B$, and their union $A \cup B$?
4. What is $(A \cap B)^c$ (the complement of the intersection of $A$ and $B$ in $S$)?
5. How would the operations change if sets $A$ and $B$ were defined over a different universal set?

Tip: To compute intersections and unions efficiently, remember that sets are unordered collections and thus do not consider repeated elements!