If we have a function $f:A \rightarrow B$, then one way to give meaning, I think, to this function, in terms of set theory, is to say, that $f$ is actually a binary relation $f=(A,B,G_f)$, where $G_f \subseteq A \times B$ is the graph of the function. Now my question is: what is $f$ if
$\bullet \ A=\emptyset, \ B\neq\emptyset$,?
$ \bullet \ B=\emptyset, \ A\neq\emptyset$ ?
$ \bullet \ B=\emptyset, \ A=\emptyset$ ?
(Another way to formulate this, I think, would be: How do the sets $\emptyset\times B,\ A\ \times \emptyset, \ \emptyset \times \emptyset $ look like ? Are they all $\emptyset$ ?)