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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.

It is given that U = {x ∈ N | 1 ≤ x ≤ 10}, A = {x ∈ U | x is an even number}, B = {x ∈ U | x is a prime number}, C = {x ∈ U | x is a factor of 24}. List the elements of the sets, and draw a Venn diagram to show the relationships between U, A, B, and C.

Explore set theory and learn to calculate intersections and unions through a problem involving even numbers, prime numbers, and factors of 24. Includes a step-by-step breakdown and a Venn diagram. Suitable for Grades 7-9.

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