(a) Prove this partial converse of Theorem 5.5.3 without using the Axiom ofChoice. Let A and B be sets with If then there existsthat is onto B.(b) Use the Axiom of Choice to prove that if there exists thenthere exists a function

B. The diameter of bones grows by the actions of both the osteoblasts and osteoclasts. 1. Osteoclasts enlarge the medullary cavity (or the density of the bone would become too heavy). 2. Osteoblasts in the periosteum build new bone around the outside. 3. So you will end up with a bone that has a larger diameter (bigger around) as well as a larger marrow cavity (more hollow). The change in diameter is known as appositional growth.