Does anyone know if the following question has been solved in general or has any insight in the question.
Let us take for example the sets {0,1} and {1,2} and function multiplication (*) over the sets shall be denoted as *(0,1)=0*1=0.
We now want to know the size of the set that can be derived from multiplication over all combinations of such sets. For example:
{*(0,0), *(0,1), *(1,0), *(1,1)} = {0,1}
where as
{*(1,1), *(1,2), *(2,1), *(2,2)} = {1,2,4}
This is a simple example but generalisations to combinations of the alphabet larger than two should be progressively more difficult to keep track of.