# Re: The Practical Benefits of the Relational Model

From: D Guntermann <guntermann_at_hotmail.com>
Date: Thu, 10 Oct 2002 16:48:08 GMT
Message-ID: <H3ryo7.J35_at_news.boeing.com>

Ohh.. That makes sense. I think I learned such properties of set operators as "set identities".

Thanks for the clarification.

Dan

"Mikito Harakiri" <mikharakiri_at_yahoo.com> wrote in message news:bdf69bdf.0210082154.6a9de1a5_at_posting.google.com...
> "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 Thu Oct 10 2002 - 18:48:08 CEST

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