Let n be a positive natural number. Let X = {iN:1in}. Denote byP(X) the power set ofX, and letP*(X) :=P(X)\ {}denote the set whose elements are subsets ofXthat are not empty. Consider the function

f:P*(X)X

which sends each non-empty subset ofXto its least element. For instance,f({1,3}) = 1. For which values ofnisfinjective, surjective, or bijective? Carefully motivate your arguments.

Problem 3. (3 points) Let 'n, be a positive natural number. Let X = {2' E N : 1 5 3' S n}. Denote by 'P(X) the power set of X , and let 73*(X) := 'P(X) \\ {0} denote the set whose elements are subsets of X that are not empty. Consider the function f: 'P" (X) ) X which sends each non-empty subset of X to its least element. For instance, f ({1,3}) = 1. For which values of n is f injective, surjective, or bijective? Carefully motivate your arguments