Question

If \( A \) and \( B \) are two sets such that \( A \times B \) consists of 6 elements, find \( B \times A \):

• A. \( \{ (1, 4), (1, 2), (4, 6) \} \)
• B. \( \{ (1, 4), (2, 6), (4, 6) \} \)
• C. \( \{ (1, 6), (2, 3), (6, 3) \} \)
• D. \( \{ (1, 2), (6, 3), (4, 6) \} \)

Hint:

The order of elements in a Cartesian product matters, so \( A \times B \) and \( B \times A \) will contain the same elements but in different orders.

Answer 1

The Correct Option is B

Step 1: Understand the Cartesian product.
The set \( A \times B \) consists of ordered pairs, and the number of elements in \( A \times B \) gives the number of pairings.
Step 2: Conclusion.
Thus, \( B \times A \) will be \( \{ (1, 4), (2, 6), (4, 6) \} \).
Final Answer: \[ \boxed{\{ (1, 4), (2, 6), (4, 6) \}} \]