$(10$ pts$.)$ Consider the following solution to the Critical Section Problem using the test$\_$and$\_$set hardware instruction.A$.$ What's the problem that Lines $6$ through $12$ are trying to solve? Briefly explain.

B$.$ The above code has two Boolean shared variables lock and waiting$[].$ What's the right initial value for each of these two variables?

lock

waiting $i$

C$.$ What's the case that is handled by Lines $9$ and $10?$ In other words, what does the condition $i==j$ mean?

D$.$ If we use a mutex semaphore instead of the test$\_$and $\_$set instruction, what will determine which of the waiting processes will enter the CS after the current process is done with it$?$