Why does the empty set not get a relation in a cartesian product

Question

As far as I understand, when $A=\{1,2\}$ and $B=\{1,2\}$, then $A \times B =\{(1,1),(1,2),(2,1),(2,2)\}$.
But $\emptyset \in A$ and $\emptyset \in B$. Are any of these valid? If not, why not?

a. $(\emptyset, 1) \in A \times B$

b. $(1, \emptyset) \in A \times B$

c. $(\emptyset, \emptyset) \in A \times B$

d. $\emptyset \in A \times B$

Answer 1

Actually, $\emptyset$ is not element of $A$ (or of $B$). The set $\emptyset$ is a subset of $A$ (and of any other set), but that's irrelevant for your question.