t are formed
by choosing x_j from X_j for j = 1 to k.

&gt; In particular, what is an element of the co-domain?
&gt; In other words, how is the codomain formed?

Domain and codomain are defined for binary relations, for example, functions.

&gt; Are you certain that you wish to use the term &quot;Cartesian Product&quot; for this relation?

I think so.

&gt; With regard to language, you assert:
&gt; &gt; Formally, I use &quot;formal language&quot; in the sense of &quot;formal language theory&quot;, e.g.:
&gt