Solution
= Solution
Partition the <power set> into disjoint classes according to <subset> size. The class of size-$i$ <subsets> has <cardinality> $\binom ni$, while the whole <power set> has <cardinality> $2^n$. Counting every <subset> once gives
$$
\boxed{\sum_{i=0}^n\binom ni=2^n.}
$$
This is also the <binomial theorem> evaluated at $1+1$, but the counting proof follows directly from the earlier parts.