To solve $A \cap (B \cap C)$, follow these steps:

Step 1: Find $B \cap C$

The intersection of sets $B$ and $C$ consists of the elements that are common to both sets.

$B = \{1, 2, 5, 4\}, \quad C = \{7, 3, 5\}$

The common element between $B$ and $C$ is $5$.

Thus, $B \cap C = \{5\}$

Step 2: Find $A \cap (B \cap C)$

Now, intersect set $A$ with $B \cap C$.

$A = \{6, 2, 4\}, \quad B \cap C = \{5\}$

Since there are no common elements between $A$ and $\{5\}$, the result is the empty set.

Thus, $A \cap (B \cap C) = \emptyset$

The answer is EMPTY.

Would you like more details or have any questions?

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Here are 5 related questions to explore:

1. What is $A \cup B$?
2. What is $(A \cap B) \cup C$?
3. What is the complement of $A$ relative to $U$?
4. Find $B \cap (A \cup C)$.
5. What is $A \cap (B \cup C)$?

Tip: When working with set operations, it helps to visualize the sets using a Venn diagram to understand their intersections and unions.