 Next, if , then divide the subsets of into two subclasses depending on whether they contain or not some fixed element in .There is an obvious bijection between these two subclasses, pairing those subsets that have the same complement relative to the subset .Also, one of these two subclasses consists of all the subsets of the set , and therefore, by the induction hypothesis, has an equal number of odd- and even-cardinality subsets.