Re: The Practical Benefits of the Relational Model

"D Guntermann" <guntermann_at_hotmail.com> wrote in message news:<H3oJuq.CE0_at_news.boeing.com>...
> 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.

For example, distributive law

A intersect B union A intersect C = A intersect (B union C)

has a dual counterpart

A union B intersect A union C = A union (B intersect C)

Same for associative law. Same for commutative law.

Proposition. If one proves a formula involving unions and intersections, then the dual formula -- where intersection and union are interchanged -- can be proven as well. Received on Wed Oct 09 2002 - 07:54:10 CEST