I think the simplest response is that SQL does return SETs. If your tables are sets. Your example tables aren't even sets so that makes the conversation that much harder to carry on.

The way I've always thought about it is that the WHERE clause defines the set, the SELECT clause defines what your VIEW of that set should show. With this view, I would never expect changing the SELECT clause to change the rows returned by they WHERE clause. I've never once been confused by this issue you talk about, they might not be "relational" by that definition but I've never actualy seen a DB claim that it implements relational theory. Conflicting definitions of relations and application of those definitions to different parts might be why you seem to be argueing for something no one else here understands. Mathematical concepts are nice, but I don't want to have to know relational theory in order to get a list of cities. SQL and all the DBs I've used provide the least amount of surpirse and the mose amount of flexibility, you can get what you want, I can get what I want, can't we all just get along? ;)

BTW Public Relations people make all those claims about what a DB can do, and who is realy suprised that PR people stretched the truth or even just plain lied? ;)

Finaly the simplist answer. You ask "Why doesn't it return a set." Answer: Returning a set based on the colums in the SELECT clause would cause more suprise than the current implementation. You are free to "group by" or "DISTINCT" in order to get your expected set though.