i) Progress
P0 executes flag[0] = true.
context switch occurs.
P1 executes flag[1] = true.
Now both the processes will be executing the while loop indefinitely.
Let's check the definition of Progress
If no process is executing in its critical section and some processes wish to enter their critical sections, then only those processes that are not executing in their remainder sections can participate in deciding which will enter its critical section next, and this selection cannot be postponed indefinitely
Here, no processes is executing in the critical section and P0, P1 want to enter the CS, but none can enter.
Hence Progress Fails.
ii) Bounded Waiting
There exists a bound, or limit, on the number of times that other processes are allowed to enter their critical sections after a process has made a request to enter its critical section and before that request is granted.
Let us suppose, process P0 is in it's critical section
context switch occurs
P1 sets flag[1] = true and enters the while() loop.
Now, when P0 completes the execution, it sets flag[0] = false, which leads to the process P1 entering into it's critical section.
Hence Bounded Waiting is Satisfied.