I'm confused on how to do the following problems for my Proofs class (Rrepresents the set of real numbers):

1. For the following equivalence relation, describe the corresponding partition.

Let ~ be the relation onR- {0} given by x ~ y iff xy > 0, for all x,y elements ofR- {0}

2. For the following partition, describe the corresponding equivalence relation.

LetDbe the partition ofR^2 consisting of all circles inR^2 centered at the origin (the origin is considered a "degenerate" circle).

For the second problem, my professor started us off by saying we should write, "Let ~ be the equivalence relation onR^2 given by (x,y) ~ (z,w) iff __________."

My professor gave a few examples but they weren't the same "style" (for lack of a better word) as the homework problems.

And, just to clarify,R- {0} is the non-zero real numbers, right?