Sets 

*A*

, 

*B*

, and 

*C*

 are subsets of the universal set 

*U*

.
These sets are defined as follows.

*U*

= 1, 2, 3, 4, 5, 6, 7, 8, 9 

*A*

= 1, 3, 4, 5, 6 

*B*

= 5, 6, 8, 9 

*C*

= 2, 3, 4, 5, 8 

Find 

∩∪*CBA*′

.
Write your answer in roster form or as 

∅

.

=∩∪*CBA*′

We are asked to find \( A' \cap (B \cup C) \), where \( A' \) represents the complement of set \( A \) relative to the universal set \( U \). Let's break down the solution step by step.

### Step 1: Find \( A' \)
The complement of set \( A \), denoted as \( A' \), includes all the elements in the universal set \( U \) that are not in \( A \).

\[
A' = U - A = \{1, 2, 3, 4, 5, 6, 7, 8, 9\} - \{1, 3, 4, 5, 6\} = \{2, 7, 8, 9\}
\]

### Step 2: Find \( B \cup C \)
Now we calculate the union of sets \( B \) and \( C \). This includes all elements that are in either \( B \), \( C \), or both.

\[
B \cup C = \{5, 6, 8, 9\} \cup \{2, 3, 4, 5, 8\} = \{2, 3, 4, 5, 6, 8, 9\}
\]

### Step 3: Find \( A' \cap (B \cup C) \)
Next, we find the intersection of \( A' \) and \( B \cup C \). This includes all elements that are in both \( A' \) and \( B \cup C \).

\[
A' \cap (B \cup C) = \{2, 7, 8, 9\} \cap \{2, 3, 4, 5, 6, 8, 9\} = \{2, 8, 9\}
\]

### Final Answer
The solution in roster form is:

\[
A' \cap (B \cup C) = \{2, 8, 9\}
\]

---

Would you like further details on any step, or do you have any questions?

Here are 5 related questions for further exploration:

1. What is the result of \( A \cap B \)?
2. How would \( A \cup B \cap C \) be evaluated?
3. What is the complement of \( B \) with respect to \( U \)?
4. Can you find \( (A \cup B)' \)?
5. What is \( (A' \cap B') \cup C' \)?

**Tip**: The complement of a set is all elements that are not in the set but are in the universal set, so it's useful to carefully define your universal set first.

Sets A, B, and C are subsets of the universal set U. These sets are defined as follows. U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 6}, B = {5, 6, 8, 9}, C = {2, 3, 4, 5, 8}. Find A' ∩ (B ∪ C). Write your answer in roster form or as ∅.

Explore how to solve the problem A' ∩ (B ∪ C) with sets A = {1, 3, 4, 5, 6}, B = {5, 6, 8, 9}, and C = {2, 3, 4, 5, 8}. Understand key set theory concepts like complements, unions, and intersections. Suitable for students in Grades 9-10.

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