Question

If $ A = \{a, b, c\}, B = \{b, c, d\} $ and $ C = \{a, d, c\} $, then $ (A - B) \times (B \cap C) $ is equal to

• A. \( \{(a, c), (a, d)\} \)
• B. \( \{(a, b), (c, d)\} \)
• C. \( \{(c, a), (d, a)\} \)
• D. \( \{(a, c), (a, d), (b, d)\} \)

Hint:

Remember that the Cartesian product involves pairing every element from the first set with every element from the second set. For difference and intersection operations, carefully evaluate the resulting sets before forming the product.

Answer 1

The Correct Option is A

Let's first solve for \( A - B \) and \( B \cap C \): \[ A - B = \{a, b, c\} - \{b, c, d\} = \{a\} \] \[ B \cap C = \{b, c, d\} \cap \{a, d, c\} = \{c, d\} \] Now, the Cartesian product of \( (A - B) \) and \( (B \cap C) \) is: \[ (A - B) \times (B \cap C) = \{a\} \times \{c, d\} = \{(a, c), (a, d)\} \] Thus, the answer is \( \{(a, c), (a, d)\} \).