i just can't comprehend what an equivalence class is. i can't even get started on this problem. maybe someone can help me atleast get started?

here's the problem

let A = {1,2,3,4,5,6} and S = power set of A

a) for a,b is an element of S, define a~b if a and b have the same number of elements. prove that ~ defines an equivalence relation on S.

b)how many equivalence class are there? list one element from each equivalence class.

i understand what an equivalence relation is. my professor gave me some hints but i can't draw anything from them.

{1,2} ~ {2,3}

{1,2,3} ~ {4,5,6}

i understand that part, but then how would i do part b?