Final answer:
It is incorrect to conclude that if A × B is a subset of C × D, then A is a subset of C and B is a subset of D, since the relationship between Cartesian products does not necessarily establish subset relationships between individual factors.
Step-by-step explanation:
The question is concerned with set theory in mathematics, specifically examining whether a subset relationship between Cartesian products implies a subset relationship between the factors of these products. To answer the question: It is not necessarily true that if A × B ⊆ C × D, then A ⊆ C and B ⊆ D. For instance, considering the Cartesian product, we see that all elements in A × B are pairs where the first element is from A and the second is from B. If A × B ⊆ C × D, it implies that every element of A × B is also an element of C × D. However, this does not ensure that all elements of A are in C, and all elements of B are in D, unless additional conditions are satisfied. In particular, the presence of the empty set as one of the factors can affect this relationship because the Cartesian product involving an empty set will always be empty regardless of the other set.