# Equivalence Relation

1. Feb 17, 2010

### Pingunoot

Moderators note: thread moved to homework area.

Please note, homework assignments or textbook style exercises for which you are seeking assistance are to be posted in the appropriate forum in our https://www.physicsforums.com/forumdisplay.php?f=152" area. This should be done whether the problem is part of one's assigned coursework or just independent study.

Let X = R × R. Define the relation R on X as follows:
(x1 , y1 )R(x2 , y2 ) iff y1 − y2 = 2(x1 − x2 ).

(a) Is it an equivalence relation?
(b) If it is, what is the equivalence class of the point (3, 1)?

I've proved this for reflexive, but I'm not sure how to go about doing it for symmetric and transitive and finding the equivalence class :S

Any guidance would be much appreciated :)

Last edited by a moderator: Apr 24, 2017
2. Feb 17, 2010

### Dick

Well, symmetric says (x1,y1)R(x2,y2) is equivalent to (x2,y2)R(x1,y1). What do those two conditions translate to? BTW, how did you prove reflexive?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook