If A = {1,2,4}, B = {2,4,5} , C = {2,5} , then `(A - C ) xx `(B - C) is equal to

Options

A. {(1,4)}
B. {(1,4), (4,4)}
C. {(4,1), (4,4)}
D. {(1,2),(2,5)}

Answer

To solve the problem, we need to find the Cartesian product of the sets \( A - C \) and \( B - C \). Let's go through the steps systematically.

### Step 1: Identify the sets
Given:
- \( A = \{1, 2, 4\} \)
- \( B = \{2, 4, 5\} \)
- \( C = \{2, 5\} \)

### Step 2: Calculate \( A - C \)
To find \( A - C \), we need to remove the elements of set \( C \) from set \( A \).
- The common element between \( A \) and \( C \) is \( 2 \).
- Therefore, we subtract \( 2 \) from \( A \).

\[ A - C = A \setminus C = \{1, 2, 4\} \setminus \{2, 5\} = \{1, 4\} \]

### Step 3: Calculate \( B - C \)
Next, we find \( B - C \) by removing the elements of set \( C \) from set \( B \).
- The common elements between \( B \) and \( C \) are \( 2 \) and \( 5 \).
- Therefore, we subtract \( 2 \) and \( 5 \) from \( B \).

\[ B - C = B \setminus C = \{2, 4, 5\} \setminus \{2, 5\} = \{4\} \]

### Step 4: Calculate the Cartesian product \( (A - C) \times (B - C) \)
Now we need to find the Cartesian product of the sets \( A - C \) and \( B - C \).

\[ (A - C) \times (B - C) = \{1, 4\} \times \{4\} \]

The Cartesian product is formed by pairing each element of the first set with each element of the second set.

- Pairing \( 1 \) with \( 4 \) gives \( (1, 4) \).
- Pairing \( 4 \) with \( 4 \) gives \( (4, 4) \).

Thus, the Cartesian product is:

\[ (A - C) \times (B - C) = \{(1, 4), (4, 4)\} \]

### Final Answer
The final answer is:

\[ \{(1, 4), (4, 4)\} \]

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