Suppose that there are two types of philosophers. One type always picks up his left fork first (a lefty), and the other type always picks up his right fork first (a righty). The behavior of a lefty is defined in Figure 6.12. The behavior of a righty is as follows: begin repeat think; wait ( fork[ (i+1) mod 5] ); wait ( fork[i] ); eat; signal ( fork[i] ); signal ( fork[ (i+1) mod 5] ); forever end; Prove the following: a. Any seating arrangement of lefties and righties with at least one of each avoids deadlock. b. Any seating arrangement of lefties and righties with at least one of each prevents starvation.