Re: The Practical Benefits of the Relational Model

hidders_at_hcoss.uia.ac.be (Jan.Hidders) wrote in message news:<3da1a630$1_at_news.uia.ac.be>...
> >Selection, Projection, and Cartesian product are primitive operations,
> >while few others - intersection, for example - could be expressed as a
> >composition of primitive ones. On the other hand, union is a notable
> >exception, so that it is introduced as an additional primitive operation to
> >form SPCU Algebra. IMHO, the fact that union is so different from
> >intersection is very disturbing. They are dual operation in the traditional
> >set theory: unions and intersections in any tautology formula can be
> >interchanged and you'll get another tautology. If they are so symmetric,
> >why they are so different in the relational theory?
>
> Symmetric? I can simulate the intersection with the difference. What is the
> corresponding operator for the union?

You mean

A intersect B = A minus (A minus B)

?

OK, let's introduce

A -> B

as a shorthand for

complement(A minus B)

Note, that we also have

A -> B = complement(A) union B

Next,

(A->B)->B = B union complement(B union complement(A))= = B union complement(B) intersect A = A union B

Therefore "->" is dual to minus, and the dual identity you were after is

A union B = (A->B)->B Received on Tue Oct 08 2002 - 12:55:13 CDT