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.