Let's start by analyzing the set operations shown in the images, based on the provided sets.

We are given the universal set $U$ and the following sets:

• $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15\}$
• $A = \{1, 3, 5, 7, 9, 11, 13, 15\}$
• $B = \{1, 2, 7, 8, 11, 12, 15\}$
• $C = \{3, 4, 6, 7, 8, 10, 14\}$
• $D = \{2, 4, 6, 8, 10, 12, 14\}$
• $E = \{5, 6, 7, 8, 10, 12, 13\}$

The questions involve set operations like union ($\cup$), intersection ($\cap$), difference ($-$), and complement ($A'$).

Solving the first few exercises:

1. $A \cup C$

   • Union combines all elements in $A$ or $C$, without repetition.
   • $A \cup C = \{1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15\}$

2. $D \cap B$

   • Intersection takes only the elements common to both sets.
   • $D \cap B = \{2, 8, 12\}$

3. $C \cup E$

   • Union combines all elements in $C$ or $E$.
   • $C \cup E = \{3, 4, 5, 6, 7, 8, 10, 12, 13, 14\}$

4. $A' \cap D$

   • $A'$ is the complement of $A$, so all elements in $U$ but not in $A$.
   • $A' = \{2, 4, 6, 8, 10, 12, 14\}$
   • $A' \cap D = \{2, 4, 6, 8, 10, 12, 14\}$ (since $A'$ and $D$ are identical)

5. $B \cup E'$

   • First, find $E'$, the complement of $E$: $E' = \{1, 2, 3, 4, 9, 11, 14, 15\}$
   • $B \cup E' = \{1, 2, 3, 4, 7, 8, 9, 11, 12, 14, 15\}$

Do you want to proceed with the next questions?

Here are 5 related questions to deepen understanding:

1. What is the result of $A \cap D$?
2. How would you calculate $B \cap E'$?
3. What is the difference between $A - B$?
4. Can you explain the result of $A' \cup C$?
5. How does set complement work in this context?

Tip: Always double-check each set element for accuracy in operations like union and intersection.