self doubt - deadlock detection - OS

Question

Isn’t it guaranteed that deadlock can be detected when there are multiple instances of resources? Sure, it cannot be detected only by looking for cycles in a resource allocation graph, but aren’t there algorithms that will always detect a deadlock, if it is there?

Answer 1

if bankers algorithm cannot lead to a safe sequence, then the state of syestem is surely deadlocked ,no matter how many instances of a single resource exist