I believe the only answer to this is Process synchronization.
Mutual exclusion is a primary priority in the Process Synchronization therefore if Process synchronization is promised, then by default Mutual Exclusion will also be.
More over Mutual exclusion is the solution to the Race Condition.
Now the entire map goes like this: Process Synchronization -> Mutual Exclusion -> Race Condition.
Which basically means if process Synchronization is promised, everything would be guaranteed.
Now with Semaphores, Counting Semaphores enables concurrent use of the semaphore variable as a result of which the Mutual exclusion may not be delivered. However, The Binary Semaphores ensure the Mutual Exclusion.
Therefore for Mutex, Answer is Process Synchronization.
and for Couting, None of the Above.
Please let me know if the mistakes