If `A = {1,4,7, 8}, B = {4, 6, 8, 9} and C = {3,4,5,7}`, then `A cap ( B - C )` is

Options

A. `{9}`
B. `{ 8,9}`
C. `{ 4, 8}`
D. `{8}`

Answer

To solve the problem, we need to find \( A \cap (B - C) \) where:

- \( A = \{1, 4, 7, 8\} \)
- \( B = \{4, 6, 8, 9\} \)
- \( C = \{3, 4, 5, 7\} \)

### Step 1: Calculate \( B - C \)

To find \( B - C \), we need to subtract the elements of set \( C \) from set \( B \). This means we will remove any elements from \( B \) that are also in \( C \).

- Elements in \( B \): \( 4, 6, 8, 9 \)
- Elements in \( C \): \( 3, 4, 5, 7 \)

Now we check each element in \( B \):
- \( 4 \) is in \( C \), so we remove it.
- \( 6 \) is not in \( C \), so we keep it.
- \( 8 \) is not in \( C \), so we keep it.
- \( 9 \) is not in \( C \), so we keep it.

Thus, \( B - C = \{6, 8, 9\} \).

### Step 2: Calculate \( A \cap (B - C) \)

Now we need to find the intersection of set \( A \) with the result from step 1, which is \( B - C = \{6, 8, 9\} \).

- Elements in \( A \): \( 1, 4, 7, 8 \)
- Elements in \( B - C \): \( 6, 8, 9 \)

Now we check for common elements:
- \( 1 \) is not in \( B - C \).
- \( 4 \) is not in \( B - C \).
- \( 7 \) is not in \( B - C \).
- \( 8 \) is in \( B - C \).

Thus, the intersection \( A \cap (B - C) = \{8\} \).

### Final Answer

The final answer is \( \{8\} \).

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