We start with the cross product set, and apply the join on criteria as a subset operation to create the "background" of the venn diagram. We can then define a

We start with the cross product set, and apply the join on criteria as a subset operation to create the "background" of the venn diagram. We can then define a set "Table A" as the subset of the cross product where (as you have written it) the first element is not null. Same for Table B and the second element. Then joins are set-union and set-intersection between these two sets. I would agree that most people just flip up the diagrams without explaining what they are actually working with.