I have a few questions regarding equivalence relations, but I don't really know how to answer them. If someone could solve and explain these two (or one) questions, it would be much appreciated.
Let P1 = {B0, B1, B2} be a partition of Z, where B0 = {3n|n ∈ Z}, B1 = {3n + 1|n ∈ Z}, and B2 = {3n + 2|n ∈ Z}. Describe the equivalence relation R1 corresponding to P1.
Let S be the set of ternary strings and let R be an equivalence relation on S. Suppose the collection of equivalence classes for R is P = {Bi|i ∈ N}, where a representative of Bi is 222...2, a ternary string of length i consisting only of twos. Describe the equivalence relation R.