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,b* ∈**R**

(2) Let *S* be the relation given by *aSb* iff sin *a* = sin *b* for all *a,b* ∈**R**

(3) Let *T* be the relation given by *aTb* iff there is some *n* ∈**Z** such that *a*=2^n *b*, for all *a,b*∈**N**

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