1. ## equivalence relations!

Hey everyone, I have some basic equivalence relation problems here that I've been trying to work on for the past while, and even though I understand the concept behind them, I'm still struggling with getting the right answers, I think. I dont expect you to answer them all, but it would be great if you could get me started!

For each of the following equivalence relations on R, find [0] and [3]

(1) Let R be the relation given by aRb iff |a|=|b| for all a,bR
(2) Let S be the relation given by aSb iff sin a = sin b for all a,bR
(3) Let T be the relation given by aTb iff there is some nZ such that a=2^n b, for all a,bN

[The answers I got for (1) are [0]={0} and [3]={-3,3}... is this correct? Thanks!]

2. Originally Posted by mrsplant
Hey everyone, I have some basic equivalence relation problems here that I've been trying to work on for the past while, and even though I understand the concept behind them, I'm still struggling with getting the right answers, I think. I dont expect you to answer them all, but it would be great if you could get me started!

For each of the following equivalence relations on R, find [0] and [3]

(1) Let R be the relation given by aRb iff |a|=|b| for all a,bR
(2) Let S be the relation given by aSb iff sin a = sin b for all a,bR
(3) Let T be the relation given by aTb iff there is some nZ such that a=2^n b, for all a,bN

[The answers I got for (1) are [0]={0} and [3]={-3,3}... is this correct? Thanks!]
$\left( {\forall n \in \mathbb{Z}} \right)\left[ {\sin (n\pi ) = 0} \right]\,\& \,\sin (x) = \sin (x + 2n\pi )$