Let S = {0,1,2,3,4,5} and let P(S)* be the set of all nonempty subsets of S. Illustrate a function m: P(S)* -> S by m(H) = the largest element in H, for any nonempty subset H of S.
a) Is m one-to-one? Why or why not?
b) Does m map P(S)* onto S? Why or why not?