March 7th, 2013, 09:01 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. 

Tags 
order, relation 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Proof that group of order 2k containts order k subgroup  Kappie  Abstract Algebra  0  April 22nd, 2012 01:52 PM 
Reduction of second order ode to first order  Grayham1990  Calculus  2  March 30th, 2012 06:24 AM 
Transform 2nd order ODE to two 1st order ODE using matrices  Norm850  Calculus  2  March 7th, 2012 04:08 PM 
If a has order hk modulo n, then a^h has order k mod n.  Jamers328  Number Theory  1  December 2nd, 2007 08:21 PM 
Relation  gaussrelatz  Algebra  0  December 31st, 1969 04:00 PM 