5. Consider the relation in N given by n~m if n and m have the same number of digits in the decimal representation. Is this an equivalence relation? If so find a partition of N in the corresponding classes of equivalence.

Let S denote the set of all 4-element permutations of the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Define an equivalence relation on S as follows: two permutations x, y = S are related if they both permute the same elements (i.e., generate the same subset). Determine the size of the equivalence class S6789 Answer = = [6789] that contains the permutation x = 6789. Enter your answer in the box below.