. Define the relation (x, y) ~ (x2, y2) in R if x + y = x + y2. Show that this is an equivalence relation. Then describe the equivalence classes. . Define a relation on R \ {(0,0)} by letting (x,) ~ (x2, y2) if there exists a nonzero such that (x1, y1) = (2x2, Ay2). Prove that defines an equivalence relation on R \ {(0,0)}. What are the equivalence classes ? ~