Utilize the product rule and sum rule to answer the following question...
How many subsets of a set with 100 elements have more than one element?
a finite set of cardinality $\displaystyle n$ has $\displaystyle 2^n$ subsets. $\displaystyle n$ of these subsets contain only one element. 1 of these subsets is $\displaystyle \emptyset$ (the empty set)