Use the given sets to find (A∩B)∩C
(
A
∩
B
)
∩
C
.

ABC={1,2,3,4,5,6,7,8}={5,7,9,11,13,15}={2,5,7,10,12,14}

We are given three sets, \( A \), \( B \), and \( C \), and the task is to find \( (A \cap B) \cap C \). Let's first break it down step by step.

### Given Sets:
- \( A = \{1, 2, 3, 4, 5, 6, 7, 8\} \)
- \( B = \{5, 7, 9, 11, 13, 15\} \)
- \( C = \{2, 5, 7, 10, 12, 14\} \)

### Step 1: Find \( A \cap B \) (the intersection of sets \( A \) and \( B \))

Intersection means the elements that are common in both sets.

\[
A \cap B = \{5, 7\}
\]
These are the only numbers present in both sets \( A \) and \( B \).

### Step 2: Find \( (A \cap B) \cap C \) (the intersection of \( A \cap B \) with \( C \))

Now we find the intersection of \( A \cap B = \{5, 7\} \) with set \( C = \{2, 5, 7, 10, 12, 14\} \).

The common elements between \( \{5, 7\} \) and \( C \) are:

\[
(A \cap B) \cap C = \{5, 7\}
\]

### Final Answer:
\[
(A \cap B) \cap C = \{5, 7\}
\]

Let me know if you would like more details on any of these steps! 

Here are 5 related questions to expand on this concept:
1. How do you find the union of sets \( A \), \( B \), and \( C \)?
2. What is the result of \( A \cup B \cup C \)?
3. How do you find \( A \setminus B \) (the difference between sets \( A \) and \( B \))?
4. What would \( (A \cup B) \cap C \) look like?
5. How do Venn diagrams help visualize set operations like intersection and union?

**Tip**: When working with set intersections, it helps to list out each element and cross-check them visually to ensure accuracy.

Use the given sets to find (A∩B)∩C: A={1,2,3,4,5,6,7,8}, B={5,7,9,11,13,15}, C={2,5,7,10,12,14}.

Learn how to solve the set theory problem (A∩B)∩C with a detailed step-by-step solution. Given sets A, B, and C, this solution demonstrates how to compute intersections of sets and provides insights into key concepts like commutativity and associativity of set intersections. Suitable for students in Grades 6-8.

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