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

Options

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

Answer

To solve the problem step by step, we need to find \( A \cap (B - C) \) given the sets:

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

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

The operation \( B - C \) means we need to remove the elements of set \( C \) from set \( B \).

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

Now, we will remove any elements in \( B \) that are also in \( C \):

- The common element between \( B \) and \( C \) is \( 4 \).

Thus, we remove \( 4 \) from \( B \):

\[ B - C = \{6, 8, 9\} \]

### 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 of \( A \): \( \{1, 4, 7, 8\} \)
- Elements of \( B - C \): \( \{6, 8, 9\} \)

The intersection \( A \cap (B - C) \) includes only the elements that are present in both sets:

- The only common element is \( 8 \).

Thus, we have:

\[ A \cap (B - C) = \{8\} \]

### Final Answer

The final result is:

\[ A \cap (B - C) = \{8\} \]

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