1. Let X = {1,2,..., 100}. Note that if P(X) is the power set of X then P(X) - {0} denotes the collection of all the nonempty subsets of X. Let f: P(X) - {0} N be given by f(A) = |A|. Here, |A| means the cardinality of A, that is, the number of elements in A. Determine if f is a function. If so, give the domain, codomain, and range. Also, if f is a function, explain why or why not it is injective.