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.

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?

Re: reflexive, anti symmetric etc... for a set

Confused about the binary relation...

Re: reflexive, anti symmetric etc... for a set

A binary relation is an oracle that says yes or no when asked if one team will beat another team during their next game. For example, you ask whether Colts will beat Patriots and the oracle says yes, then you ask whether Steelers will beat Broncos and the oracle says no. For every two teams (and it matters which team comes first) the oracle says yes or no. Here the oracle is a binary relation on teams.

For groups of students, a binary relation says yes or no given two groups. In this problem, the relation says yes if the first group is contained in the second group.