Let $\displaystyle S$ = {1,{2},{1,2}}.

My book says the following are subsets of $\displaystyle S$: {1}, {1,{2}}, {{1,2}}

I know that 1 , {2}, {1,2} are elements of S and that {2} and {1,2} are subsets of $\displaystyle S$, but I have trouble undestanding why {1}, {1,{2}}, and {{1,2}} are being subsets of $\displaystyle S$. The sets {1}, {1,{2}}, and {{1,2}} seem to me are the subsets of the power set of $\displaystyle S$, $\displaystyle P(S)$.

I am so confused.

Someone please help.