Let $N$ be the set of all subsets of {1,2,3,4}. Let
$S_0 :=\{\varnothing\}$
$S_1 :=\{\{1\},\{2\}, \{3\}, \{4\} \}$
$S_2 :=\{\{1,2\},\{1,3\}, \{1,4\}, \{2,3\}, \{2,4\}, \{3,4\} \}$
$S_3 :=\{\{1,2,3\},\{1,2,4\}, \{1,3,4\}, \{2,3,4\} \}$
$S_4 :=\{\{1,2,3,4\}\}$
show that $S_0,...,S_4$ are a partition of N and determine all the equivalence classes defined by this partition.
So it is clear that is a partition because they are pairwise disjoint and their union is $N$. (right?) but how can I determine the equivalence classes? I have read somewhere that two sets will be related if they have the same number of elements? So the the representative of equivalence classes would be $[S_0],[S_1],[S_2],[S_3],[S_4]$?