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October 27th, 2014, 02:10 PM  #1 
Newbie Joined: Feb 2014 Posts: 15 Thanks: 0  Help with Equivalence Relations
Let R be the relation on Z×Z, that is elements of this relation are pairs of pairs of integers, such that ((a,b),(c,d))∈R if and only if a+d=b+c. Show that R is an equivalence relation. So I need to show that the relation is reflexive, symmetric and transitive. For reflexive I need to show that when (a,b) E Z x Z. (a,b) = (a.b). How do I do this? I assume I have to somehow use a +d = b + c, but I'm not sure how to do it. Last edited by extreme112; October 27th, 2014 at 02:14 PM. Reason: Accidently Hit Enter 
October 27th, 2014, 02:35 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,205 Thanks: 901 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
October 27th, 2014, 03:10 PM  #3 
Newbie Joined: Feb 2014 Posts: 15 Thanks: 0  Thanks, I think I worked it out for reflexive and symmetric, but how about transitive?
Last edited by skipjack; November 11th, 2014 at 11:59 PM. 
October 27th, 2014, 03:16 PM  #4  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,205 Thanks: 901 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
(1) a + d = b + c (2) c + f = d + e From (2) we get d = c + f  e Does this give you any ideas? Dan Last edited by skipjack; November 11th, 2014 at 11:59 PM.  
October 27th, 2014, 04:02 PM  #5  
Newbie Joined: Feb 2014 Posts: 15 Thanks: 0  Quote:
Edit: I think I got the answer. If I plug in d = c+fe into d for equation (1). Then I get equation (3). Thanks for the help. Last edited by extreme112; October 27th, 2014 at 04:38 PM. Reason: I think I found the answer.  

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