My Math Forum

My Math Forum (
-   Applied Math (
-   -   Order relation (

PrototypePHX March 7th, 2013 09:01 AM

Order relation
I have the following relation:

Show that R is partially ordered. Is it totally ordered?

My solution:
It's not a total order since
A relation is partially ordered iff it is reflexive, antisymmetric and transitive.

Reflexitivity: .
This is a tautology, hence R is reflexive.

This statement is true iff x = y. That means R is antisymmetric.

Thus R is transitive.
Since R is reflexive, antisymmetric and transitive, it is partially ordered.

However I'm very unsure on the transitive part. Thanks for help.

All times are GMT -8. The time now is 12:27 PM.

Copyright © 2019 My Math Forum. All rights reserved.