$(1)$ $A \subset B$ or $A \subset C$ $\iff$ $A \subset (B \cup C)$ and
$(2)$ $(A \times B) \subset (C \times D) \implies A \subset C$
Is $(1)$ true? Or does the implication only hold in the forward direction? A friend of mine and I are beginning to work through Munkres's Topology and he is convinced it is only the forward direction, but I think it is a logical equivalence.
Munkres defines "or" to mean "either A or B or both"
$(2)$ was asked after the original question, which was $(1)$. For both questions, Brian M. Scott helped with a counterexample.