Q 28 from page 26 of Combinatorics A Guided Tour:

Define g: by the rule g(S)=|S|, where S is any subset of [2]. Write g as a set of ordered pairs.

S could be {1} {2} and {1,2}.

So for S={1} would g(S) be 1? So would that be =2 and the ordered pair would be (2,1)?

But then for S={2} the cardinality of S would again be 1 giving the ordered pair (4,1).

I don't know how to do S={1,2}.

I am confused to the nth power.

Any clues towards unwarping my brain would be greatly appreciated.