March 7th, 2013, 10:01 AM  #1 
Newbie Joined: Sep 2012 Posts: 17 Thanks: 0  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. Symmetry: This statement is true iff x = y. That means R is antisymmetric. Transitivity: 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. 

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