With respect to deadlocks in an operating system, which of the following statements is/are FALSE?

Let us analyze each statement:

• (A) Banker's algorithm is used to prevent deadlocks: FALSE. Banker's algorithm is a deadlock avoidance algorithm, which dynamically examines resource-allocation state to ensure that a circular-wait condition can never exist.

• (B) Deadlock formation can be prevented by ensuring that the hold and wait condition is not allowed: TRUE. Deadlock prevention works by invalidating at least one of the four necessary Coffman conditions (Mutual Exclusion, Hold and Wait, No Preemption, Circular Wait).

• (C) An assignment edge in a resource allocation graph is marked from a process to a resource: FALSE. In a Resource Allocation Graph (RAG), a directed edge from a resource to a process ($R_j \rightarrow P_i$) represents an assignment edge, whereas a directed edge from a process to a resource ($P_i \rightarrow R_j$) represents a request edge.

• (D) A safe state guarantees that all processes can finish without formation of a deadlock: TRUE. By definition, a system state is safe if there exists a safe sequence of processes such that every process can satisfy its maximum resource needs and terminate without deadlock.

Since the question asks for the FALSE statements, A and C are correct.