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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?
Thanks in advance. 

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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 antisymmetric, show it's reflexive.
Antisymmetric 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. 

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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 antisymmetric, show
it's reflexive.
Antisymmetric 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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