Final answer:
To prevent deadlock, the system must have enough resources to satisfy the peak demand of at least two processes. With peak demands of 3, 4, and 6 for the three processes, a minimum of 11 resources is needed (10+1 from B and C). However, since 11 is not an option, the next suitable number of resources to prevent deadlock, according to the given options, is 13.
Step-by-step explanation:
The question asks us to determine the minimum number of resources needed to prevent deadlock among three processes with different peak demands. The three processes A, B, and C have peak demands of 3, 4, and 6, respectively. To avoid deadlock in a system, one strategy is to ensure that the system has enough resources to satisfy the maximum demand of all processes except one. In this scenario, the system should satisfy the peak demand of two processes without hindering the third.
Therefore, if processes A and B have their maximum (3+4=7 resources) demand at the same time, the system must have at least one more resource than this sum for process C to make progress. So, if the maximum demand is 7, we need at least 8 resources to avoid a deadlock.
However, since process C requires 6 resources at its peak, we will consider the greater peak, which is between B and C (4+6=10 resources). Hence, to ensure that deadlock will not occur, the system needs 10 + 1 = 11 resources.
According to the options though, we do not have 11 as an option, thus we would look for the next possible higher number to avoid deadlock, which is 13. This guarantees that even if two processes are at their peak demand, the third can still obtain at least one resource and continue operation, thereby avoiding deadlock.