If A = {1, 3, 9, 10, 21), B= {4, 6, 8, 10} and C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, then the value of `A cap (B cap C)` is

Options

A. {8, 10}
B. {10}
C. None of these
D. {2, 10}

Answer

To solve the problem, we need to find the value of \( A \cap (B \cap C) \).

**Step 1: Identify the sets.**
- \( A = \{1, 3, 9, 10, 21\} \)
- \( B = \{4, 6, 8, 10\} \)
- \( C = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)

**Step 2: Find \( B \cap C \).**
To find the intersection \( B \cap C \), we look for elements that are common to both sets \( B \) and \( C \).

- Elements of \( B \): \( 4, 6, 8, 10 \)
- Elements of \( C \): \( 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 \)

Now, we check for common elements:
- \( 4 \) is in both \( B \) and \( C \)
- \( 6 \) is in both \( B \) and \( C \)
- \( 8 \) is in both \( B \) and \( C \)
- \( 10 \) is in both \( B \) and \( C \)

Thus, \( B \cap C = \{4, 6, 8, 10\} \).

**Step 3: Find \( A \cap (B \cap C) \).**
Now we need to find the intersection of set \( A \) with the result from step 2.

- Elements of \( A \): \( 1, 3, 9, 10, 21 \)
- Elements of \( B \cap C \): \( 4, 6, 8, 10 \)

Now, we check for common elements:
- \( 10 \) is in both \( A \) and \( B \cap C \)

Thus, \( A \cap (B \cap C) = \{10\} \).

**Final Answer:**
The value of \( A \cap (B \cap C) \) is \( \{10\} \).

---