Suppose that A and B are sets, and that A X B is the empty set.
How can you prove that given any set C, either A is a subset of C or B is a subset of C?
Suppose that A and B are sets, and that A X B is the empty set.
How can you prove that given any set C, either A is a subset of C or B is a subset of C?
Surely you can can show effort on this one.
Under what conditions is it ever true that $\displaystyle A \times B = \emptyset ~?$
Suppose that A and B are sets, and that A X B is the empty set. Let A = ∅ then ∅ × B = ∅ by definition, so A is a subset of C.
Let B = ∅ then A × ∅ = ∅ by definition, so B is a subset of C.