Question

Suppose that A × B = Ø, where A and B are sets. What can you conclude? (Please only choose one:) A. A = Ø or B = Ø as if any one of the sets is empty, the cartesian product of the two sets becomes Ø. B. A ≠ Ø or B ≠ Ø because if both sets are empty the product will not be given as Ø. C. A ≠ Ø and B ≠ Ø as product can be Ø if none of the set is empty. D. A = B as A = B

E. A × B = Ø

Answer 1

A. A = Ø or B = Ø

Step-by-step explanation:

If the Cartesian product of two sets A and B is empty (A × B = Ø), then either A or B (or both) must be an empty set. This is because the Cartesian product of any non-empty set with an empty set is always empty.

Therefore, we can conclude that either A is an empty set or B is an empty set, but not necessarily both. Hence, option A is the correct answer.