That's exactly it, but a more formal description seems to be expected, like: x_1,\ldots,x_n)\mapsto \{i\in\{1,\ldots,n\}|x_i=1\}" alt="fx_1,\ldots,x_n)\mapsto \{i\in\{1,\ldots,n\}|x_i=1\}" /> from to . Once you have clarified things that way, you can write the formal proof of being onto and one-to-one.