Let $S = \{1,2,3,...,10\}.$ Define the relation $\mathscr R$ on the power set $\mathscr P(S)$ of all subsets of $S$ by: for all $A,B \in \mathscr P(S),A\mathscr RB$ if and only if $N(A) = N(B)$.
Find the number of sets belonging to the equivalence class $[\{1,2\}]$.
Which is the correct way of finding this? Finding the number of 2-elements subsets of $S$ which would be ${10 \choose 2}=45$ or saying you have $10$ choices for the first element and $9$ choices for the second one thus $10 \times 9 = 90$ sets?