Re: The Practical Benefits of the Relational Model

Mikito,

Could you provide an example supporting the following statement: "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...."

I'm failing to see how set operators such as union and intersect are used in a logical expression (where the expression would result in a value that is equivalent to being vacuously true), especially in terms of interchangeability.

Thanks,

Dan

"Mikito Harakiri" <mikharakiri_at_yahoo.com> wrote in message news:bdf69bdf.0210080955.2b4af3d8_at_posting.google.com...
> 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 - 22:35:14 CEST