At a particular time of computation, the value of a counting semaphore is 7. Then 20 P operations and 'x' V operations were performed on this semaphore. If the final value of the semaphore is 5, what is x?

Explanation

Each P (wait) operation decrements a counting semaphore by 1 and each V (signal) operation increments it by 1, so the final value equals the initial value minus the number of P operations plus the number of V operations: 7 − 20 + x = 5. Solving gives x = 5 − 7 + 20 = 18, option (iii). The semaphore's value dipping below zero during the sequence is normal for a counting semaphore (it then represents the number of processes queued and waiting) and does not affect this final arithmetic.