Example 2.20 (section 2.3- Essentials of Discrete Math)

Let F be the set of all nonempty finite sets of integers, so F P(Z).

Define a function

s : F Z

by setting s(X) to be the sum of all the elements of X. For example,

s({1, 2, 3}) = 6.

a) Show that the function of Example 2.20 is not one-to-one.

b) Show that the function of Example 2.20 is onto.