Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 2, 4}, B = {1, 2, 5, 4}, and C = {7, 3, 5}. Find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
A ∩ (B ∩ C)

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.

Let U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {6, 2, 4}, B = {1, 2, 5, 4}, and C = {7, 3, 5}. Find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) A ∩ (B ∩ C)

Explore how to solve the set intersection problem involving sets A = {6, 2, 4}, B = {1, 2, 5, 4}, and C = {7, 3, 5}. Learn how to calculate A ∩ (B ∩ C) step by step using core concepts in set theory. Suitable for students in Grades 9-12.

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