(1 point) Let 𝐴={2,3,4,6,7}
 ,   𝐵={2,3,7,8}
 ,   𝐶={0,1,2,4,5,8}
.
List the elements of the following sets. If there is more than one element write them separated by commas.
𝐴∩𝐵={
 
2,3,7
 }

𝐴∪𝐵={
 
2,3,4,6,7,8
 }

(𝐵∪𝐶)∩𝐴={
 
2,3,4,7
 }

𝐵∪(𝐶∩𝐴)={
 
2,3,4,7,8
 }

Let's solve each set operation step by step.

1. **\( A \cap B \)** (Intersection of sets A and B):
   The intersection consists of elements common to both sets A and B.
   - \( A = \{2, 3, 4, 6, 7\} \)
   - \( B = \{2, 3, 7, 8\} \)
   - Common elements: \( \{2, 3, 7\} \)

   \[
   A \cap B = \{2, 3, 7\}
   \]

2. **\( A \cup B \)** (Union of sets A and B):
   The union consists of all elements from both sets A and B, without repetition.
   - \( A = \{2, 3, 4, 6, 7\} \)
   - \( B = \{2, 3, 7, 8\} \)
   - All elements: \( \{2, 3, 4, 6, 7, 8\} \)

   \[
   A \cup B = \{2, 3, 4, 6, 7, 8\}
   \]

3. **\( (B \cup C) \cap A \)** (Intersection of A with the union of B and C):
   First, find the union of B and C:
   - \( B = \{2, 3, 7, 8\} \)
   - \( C = \{0, 1, 2, 4, 5, 8\} \)
   - Union of B and C: \( \{0, 1, 2, 3, 4, 5, 7, 8\} \)

   Now, find the intersection of \( A \) with \( B \cup C \):
   - \( A = \{2, 3, 4, 6, 7\} \)
   - Common elements: \( \{2, 3, 4, 7\} \)

   \[
   (B \cup C) \cap A = \{2, 3, 4, 7\}
   \]

4. **\( B \cup (C \cap A) \)** (Union of B with the intersection of C and A):
   First, find the intersection of C and A:
   - \( C = \{0, 1, 2, 4, 5, 8\} \)
   - \( A = \{2, 3, 4, 6, 7\} \)
   - Common elements: \( \{2, 4\} \)

   Now, find the union of B with \( C \cap A \):
   - \( B = \{2, 3, 7, 8\} \)
   - \( C \cap A = \{2, 4\} \)
   - Union: \( \{2, 3, 4, 7, 8\} \)

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

### Final answers:
- \( A \cap B = \{2, 3, 7\} \)
- \( A \cup B = \{2, 3, 4, 6, 7, 8\} \)
- \( (B \cup C) \cap A = \{2, 3, 4, 7\} \)
- \( B \cup (C \cap A) = \{2, 3, 4, 7, 8\} \)

Do you want further details or explanations on any step?

Here are five related questions to deepen your understanding:
1. What is the difference between the union and intersection of sets?
2. How would you compute \( A \cap (B \cup C) \)?
3. How can Venn diagrams help visualize these set operations?
4. What happens if you find \( A \cap (B \cap C) \)?
5. How would you represent the complement of set A relative to the universal set?

**Tip:** The intersection of sets is always a subset of each set involved in the operation.

Let 𝐴={2,3,4,6,7}, 𝐵={2,3,7,8}, 𝐶={0,1,2,4,5,8}. List the elements of the following sets. If there is more than one element, write them separated by commas. 𝐴∩𝐵={2,3,7}, 𝐴∪𝐵={2,3,4,6,7,8}, (𝐵∪𝐶)∩𝐴={2,3,4,7}, 𝐵∪(𝐶∩𝐴)={2,3,4,7,8}.

Understand how to solve set operations involving union and intersection using the sets A = {2,3,4,6,7}, B = {2,3,7,8}, and C = {0,1,2,4,5,8}. The solution covers key concepts like A ∩ B, A ∪ B, (B ∪ C) ∩ A, and B ∪ (C ∩ A), suitable for students in Grades 8-10.

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