1. The problem statement, all variables and given/known data Suppose that A and B are finite sets. What is |P(AxB)|? Meaning what is the cardinality of the power set of a cartesian product of the sets A and B. 2. Relevant equations |AxB|=|A| * |B| since A and B are finite sets Power set of a set is the set of all subsets of that set, including the empty set and the set itself There are 2^|A| subsets for a set A when A is finite 3. The attempt at a solution Since A and B are finite sets, we have |AxB|=|A| * |B|. Now the power set of (AxB) is the set of all its subsets, including the empty set and the set AxB itself. Since A and B are both finite sets, there is also a finite number of subsets of (AxB). By letting C=AxB, there are exactly 2^|C| subsets. Thus |P(AxB)|=2^|AxB|=2^(|A| * |B|) This is what I have.