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October 30th, 2011, 06:05 PM  #1 
Member Joined: Nov 2010 Posts: 78 Thanks: 0  Equivalence Relation question
Hey all, need some help with the following question... Let ? be the relation on Z given by m ? n if and only if 4 divides m  n + 2. Prove or disprove the following: i) ? is reflexive So here we need to obviously show m ? m iff 4 divides m  m + 2. This would mean 4 divides 2, which is not true. So it is not reflexive, correct? ii) ? is symmetric This would mean m ? n implies n ? m....not sure where to go from here though.. if 4 divides m  n + 2 then 4 divides n  m + 2? iii) ? is transitive I would think here we have to show that if m ? n and n ? p then m ? p.... iv) Is ? an equivalence relation? It isn't, right? Since it does not satisfy all the above requirements.. 
October 30th, 2011, 06:39 PM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Equivalence Relation question Quote:
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