The problem is in Korean and involves set theory. Let's analyze and solve both questions provided in the image.

Question 03:

Given three sets

• $A = \{1, 2, 3, 4\}$,
• $B = \{2, 4, 5, 6\}$,
• $C = \{2, 3, 5, 6\}$.

We are tasked to find the number of elements in $A \cap (B \cup C)$.

Solution:

1. Find $B \cup C$:
   Combine all elements from $B$ and $C$ without duplication:
   $B \cup C = \{2, 3, 4, 5, 6\}.$

2. Find $A \cap (B \cup C)$:
   Find the intersection of $A$ and $B \cup C$, i.e., elements that are in both sets:
   $A = \{1, 2, 3, 4\}, \quad B \cup C = \{2, 3, 4, 5, 6\}.$
   Common elements are:
   $A \cap (B \cup C) = \{2, 3, 4\}.$

3. Count the number of elements in $A \cap (B \cup C)$:
   There are 3 elements: $2, 3, 4$.

Answer for Question 03:
$\boxed{3}$

Question 04:

Given a universal set $U = \{x \mid x \text{ is a natural number less than or equal to 10}\}$, and two subsets:

• $A = \{1, 2, 3, 4, 5, 6, 7\}$,
• $B = \{1, 3, 5, 7, 9\}$.

We are tasked to find the number of elements in $A' \cap B$, where $A'$ is the complement of $A$ in $U$.

Solution:

1. Find the complement of $A$, $A'$:
   Elements in $U$ but not in $A$:
   $A' = U \setminus A = \{8, 9, 10\}.$

2. Find $A' \cap B$:
   Find the intersection of $A'$ and $B$, i.e., elements that are in both sets:
   $A' = \{8, 9, 10\}, \quad B = \{1, 3, 5, 7, 9\}.$
   Common element is:
   $A' \cap B = \{9\}.$

3. Count the number of elements in $A' \cap B$:
   There is 1 element: $9$.

Answer for Question 04:
$\boxed{1}$

Recap:

• Answer for Question 03: $3$
• Answer for Question 04: $1$

Do you have any specific questions or want me to provide further explanations for any step? 😊

Related Questions:

1. How do you calculate the union and intersection of three sets?
2. What are the properties of set complements?
3. Can you solve for $(A \cup B) \setminus C$ given the same sets?
4. How does the universal set affect the complement operation?
5. Can you generalize the process of finding intersections with multiple sets?

Tip:

Always list all intermediate steps clearly when solving set theory problems to avoid confusion or missed elements!