It seems you've uploaded a handwritten question about sets and Venn diagrams. Based on the text, you're given the following:

• Set $S$ consists of integers from 1 to 12:
  $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$.
• Set $A = \{1, 3, 5, 12\}$
• Set $B = \{2, 6, 7, 8, 10, 11\}$
• Set $C = \{1, 3, 4, 6, 7, 8\}$

You are asked to illustrate this information on a Venn diagram and find the following:

1. $A \cup B$
2. $A \cup C$
3. $B \cup C$
4. $A \cap B$
5. $A \cap C$
6. $B \cap C$
7. $A'$ (complement of A)
8. $B'$ (complement of B)
9. $C'$ (complement of C)

Let's first work on each of these set operations step by step.

1. $A \cup B$ (Union of A and B)

This represents all elements that are in either set $A$ or set $B$, or in both.
So,
$A \cup B = \{1, 3, 5, 12\} \cup \{2, 6, 7, 8, 10, 11\} = \{1, 2, 3, 5, 6, 7, 8, 10, 11, 12\}$.

2. $A \cup C$ (Union of A and C)

This represents all elements that are in either set $A$ or set $C$, or in both.
So,
$A \cup C = \{1, 3, 5, 12\} \cup \{1, 3, 4, 6, 7, 8\} = \{1, 3, 4, 5, 6, 7, 8, 12\}$.

3. $B \cup C$ (Union of B and C)

This represents all elements that are in either set $B$ or set $C$, or in both.
So,
$B \cup C = \{2, 6, 7, 8, 10, 11\} \cup \{1, 3, 4, 6, 7, 8\} = \{1, 2, 3, 4, 6, 7, 8, 10, 11\}$.

4. $A \cap B$ (Intersection of A and B)

This represents all elements that are common to both sets $A$ and $B$.
So,
$A \cap B = \{1, 3, 5, 12\} \cap \{2, 6, 7, 8, 10, 11\} = \emptyset$ (no common elements).

5. $A \cap C$ (Intersection of A and C)

This represents all elements that are common to both sets $A$ and $C$.
So,
$A \cap C = \{1, 3, 5, 12\} \cap \{1, 3, 4, 6, 7, 8\} = \{1, 3\}$.

6. $B \cap C$ (Intersection of B and C)

This represents all elements that are common to both sets $B$ and $C$.
So,
$B \cap C = \{2, 6, 7, 8, 10, 11\} \cap \{1, 3, 4, 6, 7, 8\} = \{6, 7, 8\}$.

7. $A'$ (Complement of A)

The complement of $A$ contains all elements in $S$ that are not in $A$.
So,
$A' = S - A = \{2, 4, 6, 7, 8, 10, 11\}$.

8. $B'$ (Complement of B)

The complement of $B$ contains all elements in $S$ that are not in $B$.
So,
$B' = S - B = \{1, 3, 4, 5, 12\}$.

9. $C'$ (Complement of C)

The complement of $C$ contains all elements in $S$ that are not in $C$.
So,
$C' = S - C = \{2, 5, 9, 10, 11, 12\}$.

Do you want any further clarification or specific steps, like creating a Venn diagram? Let me know if you need any further breakdown or help!

Here are some additional questions for further understanding:

1. How do you visualize the union and intersection of sets in a Venn diagram?
2. Can you list the elements in the complement of a set?
3. How would you determine if two sets are disjoint using a Venn diagram?
4. What would the union of all three sets $A \cup B \cup C$ look like?
5. How do you represent the difference of sets in a Venn diagram?

Tip: When drawing a Venn diagram, remember that each circle represents a set, and the overlaps show the intersections. The space outside all circles represents the complement of the union of the sets.