P(A),X r Y
X
Ì Y or X = Y.To show that r is a partial order relation, you will need to show that r is reflexive, antisymmetric and transitive.
5. Let A = {1, 2, 3, 4} and define the relation r
on the power set of A, P(A), as follows: for X, YP(A),
X r Y X
Ì Y or X = Y.
To show that r is a partial order relation, you will need to
show that r is reflexive, antisymmetric and transitive.
Reflexive: For every X in the P(A), is X r X?
Antisymmetric: For all distinct elements X and Y of P(A), if X rY,
does this imply that Y is not related to X?
Transtive: For all elements X, Y and Z of P(A), if X r Y and Y r Z, does this imply that X r Z?