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March 7th, 2013, 09:01 AM   #1
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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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