Problem: Define a relation S on as follows: there exists a bijection s.t. .
S is an equivalence relation on (no need to prove this). Write a Representative set for the relation S. There's no need to prove that the relation you wrote is indeed a Representative set.
Reminder: Suppose is an equivalence relation over X. will be called a Representative set of T, if it occurs that: .
Attempt: I don't really know what Representative set to define. It seems to me I'm missing something simple here. I tried to look at the functions: , . None of these functions relate through relation S since there does not exist a bijection between them. I feel lost, do you have any idea what to do?