December 15, 2009 03:15 PM

Properties of Relations on Sets

Go back to T-SQL’s roots
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SQL Server Magazine
InstantDoc ID #103109
Learning the foundations of any profession will help you better understand your job and in turn further your career—and database administration is no exception. Database professionals who write a lot of T-SQL code should explore T-SQL’s foundations. SQL Server’s T-SQL is based on standard SQL, which is based on the relational model, which in turn is based on mathematical foundations (i.e., set theory and predicate logic). In this article I discuss a fundamental topic in set theo...

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Oh, well, common sence and mathematical logic don't necessary conicide. In case of empty relation we are dealing with vacuous truth it seems (http://en.wikipedia.org/wiki/Vacuous_truth).
And it this case falsehood of the antecedent doesn't affect the outcome of the conditional as long as the consequent is true.
Explainable, but not obvious.

Cheers,
Seva.

Vsevolod12/23/2009 1:32:16 PM


Itzik,
a good article overall, but..
Per defintions provided, for the data set # 3 (empty R table) relation is neither symmetric, nor asymmetric, nor transitive (it's also not non-symmetric as well).

The very first pre-requisite for each of the above mentioned definitions is (r1, r2) E R. And it is not satisfied for any of them.

Correspondingly, your question about what relation can be both symmetric and asymmetric can be answered as "none".

Best,
Seva.

Vsevolod12/23/2009 12:05:24 PM


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