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Yes, it is possible to support time-sharing without multiprogramming, though it would be highly inefficient. Time-sharing systems can allocate CPU time to a single process in a way that allows multiple users to interact with the system simultaneously, but without multiprogramming, only one user process would execute at a time. This approach would lead to significant idle time and poor resource utilization, undermining the benefits of a time-sharing system. Ultimately, multiprogramming enhances the efficiency and responsiveness of time-sharing by allowing multiple processes to coexist and utilize CPU time effectively.

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