Deadlock Detection.

$($a$)$ Show that the resource allocation state on the right side is involved in a deadlock. Indicate the set of processes involved in the deadlock.

$($b$)$ Suppose that a process $P_x$ reports to the oprating system that it is now willing to reduce its request for resource type $x(A$ or $B$ or $C$ or $D)$ by one instance. With this good news to the operating system, the system is now not deadlocked. Determine what $x$ is and what $x$ is$.$

$($c$)$ After the request by $P_x$ for $x$ is reduced by $1$ as in $($b$),$ the system is not deadlocked. Now another process $P_y$ makes a new request for an instance of $A.$ Knowing $y,$ the operating system has to declare that the system now enters a deadlocked state. Determine the identity of $y$ and explain your answer.