Assertion (A): In a Resource Allocation Graph containing multiple instances of a resource type, the presence of a cycle guarantees that a deadlock exists.
Reason (R): If multiple instances are available, a cycle represents a necessary condition for a deadlock but is not a sufficient condition.
Analysis of Assertion (A):
In a Resource Allocation Graph (RAG), if each resource type has only a single instance, a cycle is a necessary and sufficient condition for a deadlock.
However, if resources have multiple instances, a cycle may or may not result in a deadlock because processes outside the cycle might release instances and break the cycle.
Therefore, a cycle in a multi-instance graph does not guarantee a deadlock, making Assertion (A) FALSE.
Analysis of Reason (R):
When multiple instances are present, a cycle is a necessary condition (without a cycle, deadlock cannot occur), but not a sufficient condition (a cycle can exist without a deadlock).
Therefore, Reason (R) is TRUE.
Conclusion:
Assertion (A) is false, but Reason (R) is true.