Consider a system of consisting of six resources of the same type that are shared by four process. Each processneed at most 3 resources. Show that the system is deadlock free

To show that the system is deadlock-free, we can use the resource allocation graph (RAG) approach.

1. First, let's represent the resources as circles and the processes as squares in the RAG.
2. Draw a directed edge from a process to a resource if the process is currently holding that resource.
3. Draw a directed edge from a resource to a process if the resource is currently allocated to that process.
4. Now, let's analyze the RAG to check for any cycles.
5. If there are no cycles in the RAG, then the system is deadlock-free.

In this case, we have six resources and four processes. Each process needs at most three resources.

Let's assume that each process initially holds one resource. We can represent this in the RAG by drawing a directed edge from each process to a resource.

Since each process needs at most three resources, there will be at least three resources available for allocation to other processes. We can represent this in the RAG by drawing a directed edge from each available resource to a process.

Now, let's analyze the RAG. Since there are no cycles in the RAG, we can conclude that the system is deadlock-free.

Therefore, we have shown that the system consisting of six resources shared by four processes, where each process needs at most three resources, is deadlock-free.