# reflexive, anti symmetric etc... for a set

• May 23rd 2012, 04:16 PM
simwun
reflexive, anti symmetric etc... for a set
Let S be any set satisfying |S| >= 2. For any subsets X an Y of S, define a binary relation p on P(S) by:
XpY if and only if X subset Y.

for p
Give an explanation for
Is it reflexive, anti symmetric, transitive, a partial order, a total order?

I know what the above mean, but i struggle to make the link/proof to show that they are or aren't...

Any help would be much appreciated.

Thanks, Sim.
• May 23rd 2012, 04:25 PM
emakarov
Re: reflexive, anti symmetric etc... for a set
Suppose you have a group of students. All who take physics also take math, and all who take math also take philosophy. Does it follow that all who take physics also take phylosophy? This would answer the question whether p is transitive. Is it true that all students who take music also take theater or vice versa? This would answer whether p is a total order.

If you know what these type of relations mean, what exactly is your difficulty?
• May 23rd 2012, 04:33 PM
simwun
Re: reflexive, anti symmetric etc... for a set