Question

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

• A. Banker's algorithm is used to prevent deadlocks
• B. Deadlock formation can be prevented by ensuring that the hold and wait condition is not allowed
• C. An assignment edge in a resource allocation graph is marked from a process to a resource
• D. A safe state guarantees that all processes can finish without formation of a deadlock

Hint:

Separate prevention (statically ruling out one of the four Coffman conditions) from avoidance (Banker's algorithm, dynamic safe-state checking), and remember a resource-allocation-graph assignment edge always points from the resource to the process holding it, not the other way round.

Answer 1

The Correct Option is A, C

Step 1: Build a short checklist of correct deadlock facts first, then match each option against it.
Fact 1: the four Coffman conditions needed for deadlock are mutual exclusion, hold-and-wait, no preemption, and circular wait; prevention removes one of these structurally, in advance.
Fact 2: avoidance (Banker's algorithm) instead checks each request at run time against the notion of a safe state, and only grants requests that keep the system safe.
Fact 3: in a resource allocation graph, a request edge points process-to-resource ($P \rightarrow R$), and an assignment edge points resource-to-process ($R \rightarrow P$), because the assignment edge is meant to show which process currently holds that resource.
Fact 4: a safe state is, by definition, a state from which a completion ordering of all processes exists, so being in a safe state rules out deadlock.

Step 2: Match option (A) against Fact 2.
The option calls Banker's algorithm a deadlock-prevention method, but Fact 2 places it squarely in the avoidance category (it does not eliminate any of the four Coffman conditions; it dynamically tests safety before granting each request). The option's terminology is wrong, so (A) is FALSE.

Step 3: Match option (B) against Fact 1.
Disallowing hold-and-wait (for instance by forcing processes to request every resource they will need up front) is literally one of the standard ways to remove a Coffman condition, which is exactly what prevention means by Fact 1. So (B) correctly describes a valid prevention method and is TRUE, not one of the false statements.

Step 4: Match option (C) against Fact 3.
The option says the assignment edge goes from process to resource, but Fact 3 says assignment edges go from resource to process (it is the request edge that goes from process to resource). The option has swapped the two edge types, so (C) is FALSE.

Step 5: Match option (D) against Fact 4.
The option restates Fact 4 almost verbatim (safe state implies an existing completion order implies no deadlock), so (D) is TRUE, not one of the false statements.

Step 6: Collect the false ones.
$\[ \boxed{\text{(A) and (C) are the false statements}} \]$