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.