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TOMERDR
science forum beginner

Joined: 09 May 2006
Posts: 26

Posted: Mon Jul 03, 2006 7:11 am    Post subject: Where can i find problems in relations and equivalence relations?

Hi,
I am looking for problems with answers regarding relations and
equivalence Relations.

for example a good question can be:

"Is there a relation which is reflexive symetric and antisymmetric"

Btw my strategy to solve such problems is to write the definition
and using operation on sets and de morgan law to simplify it..is this a
good method?

William Elliot
science forum Guru

Joined: 24 Mar 2005
Posts: 1906

Posted: Mon Jul 03, 2006 8:23 am    Post subject: Re: Where can i find problems in relations and equivalence relations?

On Mon, 3 Jul 2006, TOMERDR wrote:

 Quote: I am looking for problems with answers regarding relations and equivalence Relations. Relations or binary relations? For the later, read about

order theory and they'll pop up all over the place.

 Quote: for example a good question can be: "Is there a relation which is reflexive symmetric and antisymmetric" Good question, got any others? Anyway yes, give an example.

If a relation is symmetric and anti-symmetric, show it's reflexive.

Anti-symmetric is a <= b, b <= a -> a = b
tho some call that asymmetric, using the former for
not(a <= b, b <= a).

 Quote: Btw my strategy to solve such problems is to write the definition and using operation on sets and de morgan law to simplify it..is this a good method? DeMorgan laws are good to know and use. In addition, you'll likely

develop other techniques.
G.E. Ivey
science forum Guru

Joined: 29 Apr 2005
Posts: 308

Posted: Mon Jul 03, 2006 4:09 pm    Post subject: Re: Where can i find problems in relations and equivalence relations?

 Quote: On Mon, 3 Jul 2006, TOMERDR wrote: I am looking for problems with answers regarding relations and equivalence Relations. Relations or binary relations? For the later, read about order theory and they'll pop up all over the place. for example a good question can be: "Is there a relation which is reflexive symmetric and antisymmetric" Good question, got any others? Anyway yes, give an example. If a relation is symmetric and anti-symmetric, show it's reflexive. Anti-symmetric is a <= b, b <= a -> a = b tho some call that asymmetric, using the former for not(a <= b, b <= a). Btw my strategy to solve such problems is to write the definition and using operation on sets and de morgan law to simplify it..is this a good method? DeMorgan laws are good to know and use. In addition, you'll likely develop other techniques.

And writing out PRECISE definitions is always a good idea!

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