https://file.aiquickdraw.com/mathbot/file/1726178066174fw38l4v6.jpg

Let's analyze the sets and operations from the image you've provided.

### Definitions from the image:
- \( U = \{ x \in \mathbb{N}, x < 14 \} \)
  - Universal set includes natural numbers less than 14: \( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13\} \)
- \( A = \{ x | x \in P \} \)
  - Set \( A \) represents prime numbers: \( A = \{2, 3, 5, 7, 11, 13\} \)
- \( B = \{ x | x \text{ is an odd number} \} \)
  - Set \( B \) includes odd numbers: \( B = \{1, 3, 5, 7, 9, 11, 13\} \)
- \( C = \{ x | x \text{ is a factor of 12} \} \)
  - Set \( C \) contains factors of 12: \( C = \{1, 2, 3, 4, 6, 12\} \)
- \( D = \{ x | x \text{ is a multiple of 3} \} \)
  - Set \( D \) contains multiples of 3: \( D = \{3, 6, 9, 12\} \)

### Answers to some of the provided operations:

1. **\( B \cap C \)**: Intersection of sets \( B \) (odd numbers) and \( C \) (factors of 12)
   - \( B \cap C = \{1, 3\} \)

2. **\( A \cup D \)**: Union of sets \( A \) (prime numbers) and \( D \) (multiples of 3)
   - \( A \cup D = \{2, 3, 5, 6, 7, 9, 11, 12, 13\} \)

3. **\( C' \)**: Complement of set \( C \) with respect to \( U \)
   - \( C' = U - C = \{5, 7, 8, 9, 10, 11, 13\} \)

4. **\( A' \)**: Complement of set \( A \) with respect to \( U \)
   - \( A' = U - A = \{1, 4, 6, 8, 9, 10, 12\} \)

Let me know if you would like further clarification or if you need solutions to the other listed operations.

Here are 5 questions to further practice:

1. What is \( A \cap B \), the intersection of sets \( A \) and \( B \)?
2. Find \( B \cap D \), the intersection of sets \( B \) and \( D \).
3. Determine \( A \cup C \), the union of sets \( A \) and \( C \).
4. Calculate \( (A \cap B) \cup D \).
5. What is \( (B \cup D) \cap A' \)?

**Tip**: When working with sets, the Venn diagram is a helpful tool to visualize the relationships among different sets.

Write the elements of the sets and perform operations such as intersections, unions, and complements using sets A (prime numbers), B (odd numbers), C (factors of 12), and D (multiples of 3) from the universal set U (natural numbers less than 14).

Learn how to write elements in roster notation and perform intersections, unions, and complements using sets A, B, C, and D from a universal set U of natural numbers less than 14. This problem covers core set theory concepts and operations suitable for Grades 7-9.

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