Consider a system of six processes. Associated with the system are 6 memory cells. The domain and range for each process is given in the following table: Process Pi Domain D (Pi) Range R (Pi) P1 M1, M2 M3 P2 M3 M4 P3 M4, M5 M6 РА M6 M1 P5 M2 M5 P6 M5, Mi M2 In addition, you are given the following precedence relation: ⇒= {(P1, P2), (P2, P3), (P1, P3), (P2, P4), (P3, P4), (P1, P5), (P5, P6)} In this notation (P1, P2) may be read P₁ → P2 which indicates that P₁ must complete before P2. a) Construct the Precedence Graph (not containing any redundant or transitive edges) Note: This is a directed-acyclic graph showing which processes must complete before another process starts. This graph may provide a partial ordering on the processes. There must not be any redundant or transitive edges (extra edges which show precedence described elsewhere). For example: P1->P2->P3 establishes an ordering. It would be wrong to list P1->P3 as an edge, as there is a transitive relationship over "->" So if you find any missing edges, just add them in for part (b). b) Determine if the system above is always determinate. If not, add to any necessary elements to make it determinate. NEVER REMOVE ITEMS FROM A PRECEDENCE RELATION YOU ARE GIVEN. Note: If the system is determinate, then indicate why you come to this conclusion. If you feel that it is not, then indicate what changes are needed to make it so.

Consider a system of six processes. Associated with the system are 6 memory cells. The domain and range for each process is given in the following table: Process Pi Domain D (Pi) Range R (Pi) P1 M1, M2 M3 P2 M3 M4 P3 M4, M5 M6 РА M6 M1 P5 M2 M5 P6 M5, Mi M2 In addition, you are given the following precedence relation: ⇒= {(P1, P2), (P2, P3), (P1, P3), (P2, P4), (P3, P4), (P1, P5), (P5, P6)} In this notation (P1, P2) may be read P₁ → P2 which indicates that P₁ must complete before P2. a) Construct the Precedence Graph (not containing any redundant or transitive edges) Note: This is a directed-acyclic graph showing which processes must complete before another process starts. This graph may provide a partial ordering on the processes. There must not be any redundant or transitive edges (extra edges which show precedence described elsewhere). For example: P1->P2->P3 establishes an ordering. It would be wrong to list P1->P3 as an edge, as there is a transitive relationship over "->" So if you find any missing edges, just add them in for part (b). b) Determine if the system above is always determinate. If not, add to any necessary elements to make it determinate. NEVER REMOVE ITEMS FROM A PRECEDENCE RELATION YOU ARE GIVEN. Note: If the system is determinate, then indicate why you come to this conclusion. If you feel that it is not, then indicate what changes are needed to make it so.