The image presents a mathematical problem involving sets and Venn diagrams. Here's a breakdown of the content:

1. Set Definitions:

   • $U = \{ x \in \mathbb{N} \mid 1 \leq x \leq 10 \}$: The universal set $U$ consists of natural numbers between 1 and 10.
   • $A = \{ x \in U \mid x \text{ is an even number} \}$: Set $A$ contains even numbers from $U$.
   • $B = \{ x \in U \mid x \text{ is a prime number} \}$: Set $B$ contains prime numbers from $U$.
   • $C = \{ x \in U \mid x \text{ is a factor of 24} \}$: Set $C$ contains numbers from $U$ that are factors of 24.

2. Tasks: a) List the elements of several sets (e.g., $U$, $A \cap B$, $A \cup C$). b) Draw a Venn diagram to show the relationships between $U$, $A$, $B$, and $C$.

I will now proceed to list the elements of these sets.Here are the elements of the sets based on the given definitions:

1. $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$
2. $A = \{2, 4, 6, 8, 10\}$ (even numbers)
3. $B = \{2, 3, 5, 7\}$ (prime numbers)
4. $C = \{1, 2, 3, 4, 6, 8\}$ (factors of 24)

For the intersection and union sets:

• $A \cap B = \{2\}$ (common to both even and prime numbers)
• $A \cup C = \{1, 2, 3, 4, 6, 8, 10\}$ (all elements either in $A$ or $C$)
• $A \cap C = \{2, 4, 6, 8\}$ (common to both $A$ and $C$)
• $A \cap (B \cup C) = \{2, 4, 6, 8\}$ (common to $A$ and either $B$ or $C$)
• $A \cap B \cap C = \{2\}$ (common to all three sets)

Would you like a Venn diagram drawn for this, or further clarification on any step?

Here are five related questions:

1. What is the union of sets $B$ and $C$?
2. Can an element belong to all sets $A$, $B$, and $C$?
3. What does the difference $A - B$ represent in this context?
4. How can the complement of set $A$ in $U$ be calculated?
5. How do intersections between sets change if we modify $C$ to be factors of a different number?

Tip: The union of sets represents all elements present in any of the involved sets, while intersections show common elements between them.