The image contains a problem involving sets and their operations. Here's the extracted content:

Given sets:

• $A = \{1, 2, 3, 5, 6\}$
• $B = \{2, 5, 7, 8\}$
• $C = \{1, 3, 5, 6, 7, 9\}$

We are asked to compute the following:

1. $A \cap (B \cup C)$
2. $(A \cap B) \cup C$

Let's solve these one by one:

1. Finding $A \cap (B \cup C)$

Step 1: Calculate $B \cup C$:

$B \cup C = \{2, 5, 7, 8\} \cup \{1, 3, 5, 6, 7, 9\}$

Combining all elements without repetition:

$B \cup C = \{1, 2, 3, 5, 6, 7, 8, 9\}$

Step 2: Calculate $A \cap (B \cup C)$:

$A \cap (B \cup C) = \{1, 2, 3, 5, 6\} \cap \{1, 2, 3, 5, 6, 7, 8, 9\}$

Finding common elements:

$A \cap (B \cup C) = \{1, 2, 3, 5, 6\}$

2. Finding $(A \cap B) \cup C$

Step 1: Calculate $A \cap B$:

$A \cap B = \{1, 2, 3, 5, 6\} \cap \{2, 5, 7, 8\}$

Finding common elements:

$A \cap B = \{2, 5\}$

Step 2: Calculate $(A \cap B) \cup C$:

$(A \cap B) \cup C = \{2, 5\} \cup \{1, 3, 5, 6, 7, 9\}$

Combining all elements without repetition:

$(A \cap B) \cup C = \{1, 2, 3, 5, 6, 7, 9\}$

Final Answers:

1. $A \cap (B \cup C) = \{1, 2, 3, 5, 6\}$
2. $(A \cap B) \cup C = \{1, 2, 3, 5, 6, 7, 9\}$

Would you like more details or have any questions?

Here are some additional questions to expand on this topic:

1. How do you find the complement of a set?
2. What is the difference between union and intersection operations?
3. How can Venn diagrams help visualize set operations?
4. What are De Morgan's laws in set theory?
5. How would the results change if we consider the universal set?

Tip: When dealing with set operations, always remember to list out all unique elements when finding unions and focus on common elements when finding intersections.